Spaces of Geodesic Triangulations of Surfaces

Abstract We give a short proof of the contractibility of the space of geodesic triangulations with fixed combinatorial type of a convex polygon in the Euclidean plane. Moreover, for any %$n>0%$, we show that there exists a space of geodesic triangulations of a polygon with a triangulation, whose...
Ausführliche Beschreibung

Abstract We give a short proof of the contractibility of the space of geodesic triangulations with fixed combinatorial type of a convex polygon in the Euclidean plane. Moreover, for any %$n>0%$, we show that there exists a space of geodesic triangulations of a polygon with a triangulation, whose n-th homotopy group is not trivial. Ausführliche Beschreibung