Sobolev Mappings, Degree, Homotopy Classes and Rational Homology Spheres

Abstract In this paper we investigate the degree and the homotopy theory of Orlicz–Sobolev mappings W1,P(M,N) between manifolds, where the Young function P satisfies a divergence condition and forms a slightly larger space than W1,n, n=dim M. In particular, we prove that if M and N are compact orien...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Goldstein, Paweł [verfasserIn] Hajłasz, Piotr

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2010

Schlagwörter:	Sobolev mappings Degree Rational homology spheres

Anmerkung:	© Mathematica Josephina, Inc. 2010

Übergeordnetes Werk:	Enthalten in: The journal of geometric analysis - New York, NY : Springer, 1991, 22(2010), 2 vom: 11. Nov., Seite 320-338
Übergeordnetes Werk:	volume:22 ; year:2010 ; number:2 ; day:11 ; month:11 ; pages:320-338

Links:	Volltext

DOI / URN:	10.1007/s12220-010-9194-4

Katalog-ID:	SPR025403265

Internformat


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publishDate	2010
allfields	10.1007/s12220-010-9194-4 doi (DE-627)SPR025403265 (SPR)s12220-010-9194-4-e DE-627 ger DE-627 rakwb eng Goldstein, Paweł verfasserin aut Sobolev Mappings, Degree, Homotopy Classes and Rational Homology Spheres 2010 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Mathematica Josephina, Inc. 2010 Abstract In this paper we investigate the degree and the homotopy theory of Orlicz–Sobolev mappings W1,P(M,N) between manifolds, where the Young function P satisfies a divergence condition and forms a slightly larger space than W1,n, n=dim M. In particular, we prove that if M and N are compact oriented manifolds without boundary and dim M=dim N=n, then the degree is well defined in W1,P(M,N) if and only if the universal cover of N is not a rational homology sphere, and in the case n=4, if and only if N is not homeomorphic to S4. Sobolev mappings (dpeaa)DE-He213 Degree (dpeaa)DE-He213 Rational homology spheres (dpeaa)DE-He213 Hajłasz, Piotr aut Enthalten in The journal of geometric analysis New York, NY : Springer, 1991 22(2010), 2 vom: 11. Nov., Seite 320-338 (DE-627)496971867 (DE-600)2199635-0 1559-002X nnns volume:22 year:2010 number:2 day:11 month:11 pages:320-338 https://dx.doi.org/10.1007/s12220-010-9194-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 22 2010 2 11 11 320-338
spelling	10.1007/s12220-010-9194-4 doi (DE-627)SPR025403265 (SPR)s12220-010-9194-4-e DE-627 ger DE-627 rakwb eng Goldstein, Paweł verfasserin aut Sobolev Mappings, Degree, Homotopy Classes and Rational Homology Spheres 2010 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Mathematica Josephina, Inc. 2010 Abstract In this paper we investigate the degree and the homotopy theory of Orlicz–Sobolev mappings W1,P(M,N) between manifolds, where the Young function P satisfies a divergence condition and forms a slightly larger space than W1,n, n=dim M. In particular, we prove that if M and N are compact oriented manifolds without boundary and dim M=dim N=n, then the degree is well defined in W1,P(M,N) if and only if the universal cover of N is not a rational homology sphere, and in the case n=4, if and only if N is not homeomorphic to S4. Sobolev mappings (dpeaa)DE-He213 Degree (dpeaa)DE-He213 Rational homology spheres (dpeaa)DE-He213 Hajłasz, Piotr aut Enthalten in The journal of geometric analysis New York, NY : Springer, 1991 22(2010), 2 vom: 11. Nov., Seite 320-338 (DE-627)496971867 (DE-600)2199635-0 1559-002X nnns volume:22 year:2010 number:2 day:11 month:11 pages:320-338 https://dx.doi.org/10.1007/s12220-010-9194-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 22 2010 2 11 11 320-338
allfields_unstemmed	10.1007/s12220-010-9194-4 doi (DE-627)SPR025403265 (SPR)s12220-010-9194-4-e DE-627 ger DE-627 rakwb eng Goldstein, Paweł verfasserin aut Sobolev Mappings, Degree, Homotopy Classes and Rational Homology Spheres 2010 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Mathematica Josephina, Inc. 2010 Abstract In this paper we investigate the degree and the homotopy theory of Orlicz–Sobolev mappings W1,P(M,N) between manifolds, where the Young function P satisfies a divergence condition and forms a slightly larger space than W1,n, n=dim M. In particular, we prove that if M and N are compact oriented manifolds without boundary and dim M=dim N=n, then the degree is well defined in W1,P(M,N) if and only if the universal cover of N is not a rational homology sphere, and in the case n=4, if and only if N is not homeomorphic to S4. Sobolev mappings (dpeaa)DE-He213 Degree (dpeaa)DE-He213 Rational homology spheres (dpeaa)DE-He213 Hajłasz, Piotr aut Enthalten in The journal of geometric analysis New York, NY : Springer, 1991 22(2010), 2 vom: 11. Nov., Seite 320-338 (DE-627)496971867 (DE-600)2199635-0 1559-002X nnns volume:22 year:2010 number:2 day:11 month:11 pages:320-338 https://dx.doi.org/10.1007/s12220-010-9194-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 22 2010 2 11 11 320-338
allfieldsGer	10.1007/s12220-010-9194-4 doi (DE-627)SPR025403265 (SPR)s12220-010-9194-4-e DE-627 ger DE-627 rakwb eng Goldstein, Paweł verfasserin aut Sobolev Mappings, Degree, Homotopy Classes and Rational Homology Spheres 2010 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Mathematica Josephina, Inc. 2010 Abstract In this paper we investigate the degree and the homotopy theory of Orlicz–Sobolev mappings W1,P(M,N) between manifolds, where the Young function P satisfies a divergence condition and forms a slightly larger space than W1,n, n=dim M. In particular, we prove that if M and N are compact oriented manifolds without boundary and dim M=dim N=n, then the degree is well defined in W1,P(M,N) if and only if the universal cover of N is not a rational homology sphere, and in the case n=4, if and only if N is not homeomorphic to S4. Sobolev mappings (dpeaa)DE-He213 Degree (dpeaa)DE-He213 Rational homology spheres (dpeaa)DE-He213 Hajłasz, Piotr aut Enthalten in The journal of geometric analysis New York, NY : Springer, 1991 22(2010), 2 vom: 11. Nov., Seite 320-338 (DE-627)496971867 (DE-600)2199635-0 1559-002X nnns volume:22 year:2010 number:2 day:11 month:11 pages:320-338 https://dx.doi.org/10.1007/s12220-010-9194-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 22 2010 2 11 11 320-338
allfieldsSound	10.1007/s12220-010-9194-4 doi (DE-627)SPR025403265 (SPR)s12220-010-9194-4-e DE-627 ger DE-627 rakwb eng Goldstein, Paweł verfasserin aut Sobolev Mappings, Degree, Homotopy Classes and Rational Homology Spheres 2010 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Mathematica Josephina, Inc. 2010 Abstract In this paper we investigate the degree and the homotopy theory of Orlicz–Sobolev mappings W1,P(M,N) between manifolds, where the Young function P satisfies a divergence condition and forms a slightly larger space than W1,n, n=dim M. In particular, we prove that if M and N are compact oriented manifolds without boundary and dim M=dim N=n, then the degree is well defined in W1,P(M,N) if and only if the universal cover of N is not a rational homology sphere, and in the case n=4, if and only if N is not homeomorphic to S4. Sobolev mappings (dpeaa)DE-He213 Degree (dpeaa)DE-He213 Rational homology spheres (dpeaa)DE-He213 Hajłasz, Piotr aut Enthalten in The journal of geometric analysis New York, NY : Springer, 1991 22(2010), 2 vom: 11. Nov., Seite 320-338 (DE-627)496971867 (DE-600)2199635-0 1559-002X nnns volume:22 year:2010 number:2 day:11 month:11 pages:320-338 https://dx.doi.org/10.1007/s12220-010-9194-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 22 2010 2 11 11 320-338
language	English
source	Enthalten in The journal of geometric analysis 22(2010), 2 vom: 11. Nov., Seite 320-338 volume:22 year:2010 number:2 day:11 month:11 pages:320-338
sourceStr	Enthalten in The journal of geometric analysis 22(2010), 2 vom: 11. Nov., Seite 320-338 volume:22 year:2010 number:2 day:11 month:11 pages:320-338
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Sobolev mappings Degree Rational homology spheres
isfreeaccess_bool	false
container_title	The journal of geometric analysis
authorswithroles_txt_mv	Goldstein, Paweł @@aut@@ Hajłasz, Piotr @@aut@@
publishDateDaySort_date	2010-11-11T00:00:00Z
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author	Goldstein, Paweł
spellingShingle	Goldstein, Paweł misc Sobolev mappings misc Degree misc Rational homology spheres Sobolev Mappings, Degree, Homotopy Classes and Rational Homology Spheres
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topic_title	Sobolev Mappings, Degree, Homotopy Classes and Rational Homology Spheres Sobolev mappings (dpeaa)DE-He213 Degree (dpeaa)DE-He213 Rational homology spheres (dpeaa)DE-He213
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title	Sobolev Mappings, Degree, Homotopy Classes and Rational Homology Spheres
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title_full	Sobolev Mappings, Degree, Homotopy Classes and Rational Homology Spheres
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author_browse	Goldstein, Paweł Hajłasz, Piotr
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doi_str_mv	10.1007/s12220-010-9194-4
title_sort	sobolev mappings, degree, homotopy classes and rational homology spheres
title_auth	Sobolev Mappings, Degree, Homotopy Classes and Rational Homology Spheres
abstract	Abstract In this paper we investigate the degree and the homotopy theory of Orlicz–Sobolev mappings W1,P(M,N) between manifolds, where the Young function P satisfies a divergence condition and forms a slightly larger space than W1,n, n=dim M. In particular, we prove that if M and N are compact oriented manifolds without boundary and dim M=dim N=n, then the degree is well defined in W1,P(M,N) if and only if the universal cover of N is not a rational homology sphere, and in the case n=4, if and only if N is not homeomorphic to S4. © Mathematica Josephina, Inc. 2010
abstractGer	Abstract In this paper we investigate the degree and the homotopy theory of Orlicz–Sobolev mappings W1,P(M,N) between manifolds, where the Young function P satisfies a divergence condition and forms a slightly larger space than W1,n, n=dim M. In particular, we prove that if M and N are compact oriented manifolds without boundary and dim M=dim N=n, then the degree is well defined in W1,P(M,N) if and only if the universal cover of N is not a rational homology sphere, and in the case n=4, if and only if N is not homeomorphic to S4. © Mathematica Josephina, Inc. 2010
abstract_unstemmed	Abstract In this paper we investigate the degree and the homotopy theory of Orlicz–Sobolev mappings W1,P(M,N) between manifolds, where the Young function P satisfies a divergence condition and forms a slightly larger space than W1,n, n=dim M. In particular, we prove that if M and N are compact oriented manifolds without boundary and dim M=dim N=n, then the degree is well defined in W1,P(M,N) if and only if the universal cover of N is not a rational homology sphere, and in the case n=4, if and only if N is not homeomorphic to S4. © Mathematica Josephina, Inc. 2010
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title_short	Sobolev Mappings, Degree, Homotopy Classes and Rational Homology Spheres
url	https://dx.doi.org/10.1007/s12220-010-9194-4
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up_date	2024-07-03T15:47:40.993Z
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fullrecord_marcxml	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR025403265</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230403070343.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201007s2010 xx \|\|\|\|\|o 00\| \|\|eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s12220-010-9194-4</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR025403265</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s12220-010-9194-4-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Goldstein, Paweł</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Sobolev Mappings, Degree, Homotopy Classes and Rational Homology Spheres</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2010</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Mathematica Josephina, Inc. 2010</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract In this paper we investigate the degree and the homotopy theory of Orlicz–Sobolev mappings W1,P(M,N) between manifolds, where the Young function P satisfies a divergence condition and forms a slightly larger space than W1,n, n=dim M. In particular, we prove that if M and N are compact oriented manifolds without boundary and dim M=dim N=n, then the degree is well defined in W1,P(M,N) if and only if the universal cover of N is not a rational homology sphere, and in the case n=4, if and only if N is not homeomorphic to S4.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Sobolev mappings</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Degree</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Rational homology spheres</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Hajłasz, Piotr</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">The journal of geometric analysis</subfield><subfield code="d">New York, NY : Springer, 1991</subfield><subfield code="g">22(2010), 2 vom: 11. 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