Spaces of Geodesic Triangulations of Surfaces

2019/10/07 by Luo, Yanwen
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1910.03070

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.

Related

• Spaces of Geodesic Triangulations Are Cells
• A note on graph drawings with star-shaped boundaries in the plane
• Characterisation of geodesic self-dual regular surface triangulations
• Geometries of convex and finite sets of geodesic spaces
• Shapes of polyhedra and triangulations of the sphere