The Space of Vectored Hyperbolic Surfaces is Path-Connected

2023/11/28 by Warakkagun, Sangsan
#57K20 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2311.16667

Abstract

In the space H² of hyperbolic surfaces decorated with a base unit vector, the topology induced by the Gromov-Hausdorff convergence coincides with the Chabauty topology on the space of discrete torsion-free subgroups of \rmPSL₂(ℝ). Using paths constructed from changing the Fenchel-Nielsen coordinates and shrinking simple closed curves to cusps, we demonstrate path-connectivity of H² and some of its subspaces.

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