The braid group

Let n , m ∈ N , and let B n ,...
Ausführliche Beschreibung

Let n , m ∈ N , and let B n , m ( R P 2 ) be the set of ( n + m ) -braids of the projective plane whose associated permutation lies in the subgroup S n × S m of the symmetric group S n + m . We study the splitting problem of the following generalisation of the Fadell–Neuwirth short exact sequence: 1 → B m ( R P 2 ∖ { x 1 , … , x n } ) → B n , m ( R P 2 ) → q ¯ B n ( R P 2 ) → 1 , where the map q ¯ can be considered geometrically as the epimorphism that forgets the last m strands, as well as the existence of a section of the corresponding fibration q : F n + m ( R P 2 ) / S n × S m → F n ( R P 2 ) / S n , where we denote by F n ( R P 2 ) the n t h ordered configuration space of the projective plane R P 2 . Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Makri, Stavroula [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2022

Schlagwörter:	Surface braid group Group presentation Fadell–Neuwirth short exact sequence Section problem Fibration Residually nilpotent Residually solvable

Übergeordnetes Werk:	Enthalten in: Topology and its applications - Amsterdam [u.a.] : Elsevier, 1980, 318
Übergeordnetes Werk:	volume:318

DOI / URN:	10.1016/j.topol.2022.108202

Katalog-ID:	ELV008336431

Internformat


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245	1	0	\|a The braid group
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520			\|a Let n , m ∈ N , and let B n , m ( R P 2 ) be the set of ( n + m ) -braids of the projective plane whose associated permutation lies in the subgroup S n × S m of the symmetric group S n + m . We study the splitting problem of the following generalisation of the Fadell–Neuwirth short exact sequence: 1 → B m ( R P 2 ∖ { x 1 , … , x n } ) → B n , m ( R P 2 ) → q ¯ B n ( R P 2 ) → 1 , where the map q ¯ can be considered geometrically as the epimorphism that forgets the last m strands, as well as the existence of a section of the corresponding fibration q : F n + m ( R P 2 ) / S n × S m → F n ( R P 2 ) / S n , where we denote by F n ( R P 2 ) the n t h ordered configuration space of the projective plane R P 2 .
650		4	\|a Surface braid group
650		4	\|a Group presentation
650		4	\|a Fadell–Neuwirth short exact sequence
650		4	\|a Section problem
650		4	\|a Fibration
650		4	\|a Residually nilpotent
650		4	\|a Residually solvable
773	0	8	\|i Enthalten in \|t Topology and its applications \|d Amsterdam [u.a.] : Elsevier, 1980 \|g 318 \|h Online-Ressource \|w (DE-627)306652862 \|w (DE-600)1499758-7 \|w (DE-576)081954425 \|7 nnns
773	1	8	\|g volume:318
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912			\|a GBV_ILN_23
912			\|a GBV_ILN_24
912			\|a GBV_ILN_31
912			\|a GBV_ILN_32
912			\|a GBV_ILN_40
912			\|a GBV_ILN_60
912			\|a GBV_ILN_62
912			\|a GBV_ILN_63
912			\|a GBV_ILN_65
912			\|a GBV_ILN_69
912			\|a GBV_ILN_70
912			\|a GBV_ILN_73
912			\|a GBV_ILN_74
912			\|a GBV_ILN_90
912			\|a GBV_ILN_95
912			\|a GBV_ILN_100
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_224
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2038
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2056
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2065
912			\|a GBV_ILN_2068
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2113
912			\|a GBV_ILN_2118
912			\|a GBV_ILN_2122
912			\|a GBV_ILN_2129
912			\|a GBV_ILN_2143
912			\|a GBV_ILN_2147
912			\|a GBV_ILN_2148
912			\|a GBV_ILN_2152
912			\|a GBV_ILN_2153
912			\|a GBV_ILN_2190
912			\|a GBV_ILN_2336
912			\|a GBV_ILN_2507
912			\|a GBV_ILN_2522
912			\|a GBV_ILN_4012
912			\|a GBV_ILN_4035
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4125
912			\|a GBV_ILN_4126
912			\|a GBV_ILN_4242
912			\|a GBV_ILN_4249
912			\|a GBV_ILN_4251
912			\|a GBV_ILN_4305
912			\|a GBV_ILN_4306
912			\|a GBV_ILN_4307
912			\|a GBV_ILN_4313
912			\|a GBV_ILN_4322
912			\|a GBV_ILN_4323
912			\|a GBV_ILN_4324
912			\|a GBV_ILN_4325
912			\|a GBV_ILN_4326
912			\|a GBV_ILN_4333
912			\|a GBV_ILN_4334
912			\|a GBV_ILN_4335
912			\|a GBV_ILN_4338
912			\|a GBV_ILN_4367
912			\|a GBV_ILN_4393
912			\|a GBV_ILN_4700
936	b	k	\|a 31.50 \|j Geometrie: Allgemeines
936	b	k	\|a 31.60 \|j Topologie: Allgemeines
951			\|a AR
952			\|d 318

Indexfelder

author_variant	s m sm
matchkey_str	makristavroula:2022----:hbad
hierarchy_sort_str	2022
bklnumber	31.50 31.60
publishDate	2022
allfields	10.1016/j.topol.2022.108202 doi (DE-627)ELV008336431 (ELSEVIER)S0166-8641(22)00204-8 DE-627 ger DE-627 rda eng 510 DE-600 31.50 bkl 31.60 bkl Makri, Stavroula verfasserin (orcid)0000-0002-4156-7789 aut The braid group 2022 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Let n , m ∈ N , and let B n , m ( R P 2 ) be the set of ( n + m ) -braids of the projective plane whose associated permutation lies in the subgroup S n × S m of the symmetric group S n + m . We study the splitting problem of the following generalisation of the Fadell–Neuwirth short exact sequence: 1 → B m ( R P 2 ∖ { x 1 , … , x n } ) → B n , m ( R P 2 ) → q ¯ B n ( R P 2 ) → 1 , where the map q ¯ can be considered geometrically as the epimorphism that forgets the last m strands, as well as the existence of a section of the corresponding fibration q : F n + m ( R P 2 ) / S n × S m → F n ( R P 2 ) / S n , where we denote by F n ( R P 2 ) the n t h ordered configuration space of the projective plane R P 2 . Surface braid group Group presentation Fadell–Neuwirth short exact sequence Section problem Fibration Residually nilpotent Residually solvable Enthalten in Topology and its applications Amsterdam [u.a.] : Elsevier, 1980 318 Online-Ressource (DE-627)306652862 (DE-600)1499758-7 (DE-576)081954425 nnns volume:318 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 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_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.50 Geometrie: Allgemeines 31.60 Topologie: Allgemeines AR 318
spelling	10.1016/j.topol.2022.108202 doi (DE-627)ELV008336431 (ELSEVIER)S0166-8641(22)00204-8 DE-627 ger DE-627 rda eng 510 DE-600 31.50 bkl 31.60 bkl Makri, Stavroula verfasserin (orcid)0000-0002-4156-7789 aut The braid group 2022 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Let n , m ∈ N , and let B n , m ( R P 2 ) be the set of ( n + m ) -braids of the projective plane whose associated permutation lies in the subgroup S n × S m of the symmetric group S n + m . We study the splitting problem of the following generalisation of the Fadell–Neuwirth short exact sequence: 1 → B m ( R P 2 ∖ { x 1 , … , x n } ) → B n , m ( R P 2 ) → q ¯ B n ( R P 2 ) → 1 , where the map q ¯ can be considered geometrically as the epimorphism that forgets the last m strands, as well as the existence of a section of the corresponding fibration q : F n + m ( R P 2 ) / S n × S m → F n ( R P 2 ) / S n , where we denote by F n ( R P 2 ) the n t h ordered configuration space of the projective plane R P 2 . Surface braid group Group presentation Fadell–Neuwirth short exact sequence Section problem Fibration Residually nilpotent Residually solvable Enthalten in Topology and its applications Amsterdam [u.a.] : Elsevier, 1980 318 Online-Ressource (DE-627)306652862 (DE-600)1499758-7 (DE-576)081954425 nnns volume:318 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 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_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.50 Geometrie: Allgemeines 31.60 Topologie: Allgemeines AR 318
allfields_unstemmed	10.1016/j.topol.2022.108202 doi (DE-627)ELV008336431 (ELSEVIER)S0166-8641(22)00204-8 DE-627 ger DE-627 rda eng 510 DE-600 31.50 bkl 31.60 bkl Makri, Stavroula verfasserin (orcid)0000-0002-4156-7789 aut The braid group 2022 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Let n , m ∈ N , and let B n , m ( R P 2 ) be the set of ( n + m ) -braids of the projective plane whose associated permutation lies in the subgroup S n × S m of the symmetric group S n + m . We study the splitting problem of the following generalisation of the Fadell–Neuwirth short exact sequence: 1 → B m ( R P 2 ∖ { x 1 , … , x n } ) → B n , m ( R P 2 ) → q ¯ B n ( R P 2 ) → 1 , where the map q ¯ can be considered geometrically as the epimorphism that forgets the last m strands, as well as the existence of a section of the corresponding fibration q : F n + m ( R P 2 ) / S n × S m → F n ( R P 2 ) / S n , where we denote by F n ( R P 2 ) the n t h ordered configuration space of the projective plane R P 2 . Surface braid group Group presentation Fadell–Neuwirth short exact sequence Section problem Fibration Residually nilpotent Residually solvable Enthalten in Topology and its applications Amsterdam [u.a.] : Elsevier, 1980 318 Online-Ressource (DE-627)306652862 (DE-600)1499758-7 (DE-576)081954425 nnns volume:318 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 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_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.50 Geometrie: Allgemeines 31.60 Topologie: Allgemeines AR 318
allfieldsGer	10.1016/j.topol.2022.108202 doi (DE-627)ELV008336431 (ELSEVIER)S0166-8641(22)00204-8 DE-627 ger DE-627 rda eng 510 DE-600 31.50 bkl 31.60 bkl Makri, Stavroula verfasserin (orcid)0000-0002-4156-7789 aut The braid group 2022 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Let n , m ∈ N , and let B n , m ( R P 2 ) be the set of ( n + m ) -braids of the projective plane whose associated permutation lies in the subgroup S n × S m of the symmetric group S n + m . We study the splitting problem of the following generalisation of the Fadell–Neuwirth short exact sequence: 1 → B m ( R P 2 ∖ { x 1 , … , x n } ) → B n , m ( R P 2 ) → q ¯ B n ( R P 2 ) → 1 , where the map q ¯ can be considered geometrically as the epimorphism that forgets the last m strands, as well as the existence of a section of the corresponding fibration q : F n + m ( R P 2 ) / S n × S m → F n ( R P 2 ) / S n , where we denote by F n ( R P 2 ) the n t h ordered configuration space of the projective plane R P 2 . Surface braid group Group presentation Fadell–Neuwirth short exact sequence Section problem Fibration Residually nilpotent Residually solvable Enthalten in Topology and its applications Amsterdam [u.a.] : Elsevier, 1980 318 Online-Ressource (DE-627)306652862 (DE-600)1499758-7 (DE-576)081954425 nnns volume:318 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 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_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.50 Geometrie: Allgemeines 31.60 Topologie: Allgemeines AR 318
allfieldsSound	10.1016/j.topol.2022.108202 doi (DE-627)ELV008336431 (ELSEVIER)S0166-8641(22)00204-8 DE-627 ger DE-627 rda eng 510 DE-600 31.50 bkl 31.60 bkl Makri, Stavroula verfasserin (orcid)0000-0002-4156-7789 aut The braid group 2022 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Let n , m ∈ N , and let B n , m ( R P 2 ) be the set of ( n + m ) -braids of the projective plane whose associated permutation lies in the subgroup S n × S m of the symmetric group S n + m . We study the splitting problem of the following generalisation of the Fadell–Neuwirth short exact sequence: 1 → B m ( R P 2 ∖ { x 1 , … , x n } ) → B n , m ( R P 2 ) → q ¯ B n ( R P 2 ) → 1 , where the map q ¯ can be considered geometrically as the epimorphism that forgets the last m strands, as well as the existence of a section of the corresponding fibration q : F n + m ( R P 2 ) / S n × S m → F n ( R P 2 ) / S n , where we denote by F n ( R P 2 ) the n t h ordered configuration space of the projective plane R P 2 . Surface braid group Group presentation Fadell–Neuwirth short exact sequence Section problem Fibration Residually nilpotent Residually solvable Enthalten in Topology and its applications Amsterdam [u.a.] : Elsevier, 1980 318 Online-Ressource (DE-627)306652862 (DE-600)1499758-7 (DE-576)081954425 nnns volume:318 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 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_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.50 Geometrie: Allgemeines 31.60 Topologie: Allgemeines AR 318
language	English
source	Enthalten in Topology and its applications 318 volume:318
sourceStr	Enthalten in Topology and its applications 318 volume:318
format_phy_str_mv	Article
bklname	Geometrie: Allgemeines Topologie: Allgemeines
institution	findex.gbv.de
topic_facet	Surface braid group Group presentation Fadell–Neuwirth short exact sequence Section problem Fibration Residually nilpotent Residually solvable
dewey-raw	510
isfreeaccess_bool	false
container_title	Topology and its applications
authorswithroles_txt_mv	Makri, Stavroula @@aut@@
publishDateDaySort_date	2022-01-01T00:00:00Z
hierarchy_top_id	306652862
dewey-sort	3510
id	ELV008336431
language_de	englisch
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author	Makri, Stavroula
spellingShingle	Makri, Stavroula ddc 510 bkl 31.50 bkl 31.60 misc Surface braid group misc Group presentation misc Fadell–Neuwirth short exact sequence misc Section problem misc Fibration misc Residually nilpotent misc Residually solvable The braid group
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topic_title	510 DE-600 31.50 bkl 31.60 bkl The braid group Surface braid group Group presentation Fadell–Neuwirth short exact sequence Section problem Fibration Residually nilpotent Residually solvable
topic	ddc 510 bkl 31.50 bkl 31.60 misc Surface braid group misc Group presentation misc Fadell–Neuwirth short exact sequence misc Section problem misc Fibration misc Residually nilpotent misc Residually solvable
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format_facet	Elektronische Aufsätze Aufsätze Elektronische Ressource
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title	The braid group
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title_full	The braid group
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title_auth	The braid group
abstract	Let n , m ∈ N , and let B n , m ( R P 2 ) be the set of ( n + m ) -braids of the projective plane whose associated permutation lies in the subgroup S n × S m of the symmetric group S n + m . We study the splitting problem of the following generalisation of the Fadell–Neuwirth short exact sequence: 1 → B m ( R P 2 ∖ { x 1 , … , x n } ) → B n , m ( R P 2 ) → q ¯ B n ( R P 2 ) → 1 , where the map q ¯ can be considered geometrically as the epimorphism that forgets the last m strands, as well as the existence of a section of the corresponding fibration q : F n + m ( R P 2 ) / S n × S m → F n ( R P 2 ) / S n , where we denote by F n ( R P 2 ) the n t h ordered configuration space of the projective plane R P 2 .
abstractGer	Let n , m ∈ N , and let B n , m ( R P 2 ) be the set of ( n + m ) -braids of the projective plane whose associated permutation lies in the subgroup S n × S m of the symmetric group S n + m . We study the splitting problem of the following generalisation of the Fadell–Neuwirth short exact sequence: 1 → B m ( R P 2 ∖ { x 1 , … , x n } ) → B n , m ( R P 2 ) → q ¯ B n ( R P 2 ) → 1 , where the map q ¯ can be considered geometrically as the epimorphism that forgets the last m strands, as well as the existence of a section of the corresponding fibration q : F n + m ( R P 2 ) / S n × S m → F n ( R P 2 ) / S n , where we denote by F n ( R P 2 ) the n t h ordered configuration space of the projective plane R P 2 .
abstract_unstemmed	Let n , m ∈ N , and let B n , m ( R P 2 ) be the set of ( n + m ) -braids of the projective plane whose associated permutation lies in the subgroup S n × S m of the symmetric group S n + m . We study the splitting problem of the following generalisation of the Fadell–Neuwirth short exact sequence: 1 → B m ( R P 2 ∖ { x 1 , … , x n } ) → B n , m ( R P 2 ) → q ¯ B n ( R P 2 ) → 1 , where the map q ¯ can be considered geometrically as the epimorphism that forgets the last m strands, as well as the existence of a section of the corresponding fibration q : F n + m ( R P 2 ) / S n × S m → F n ( R P 2 ) / S n , where we denote by F n ( R P 2 ) the n t h ordered configuration space of the projective plane R P 2 .
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title_short	The braid group
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up_date	2024-07-06T19:21:16.431Z
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