Characterizing candidates for Cannon's Conjecture from Geometric Measure Theory
Geometric Topology
2023-02-27 v2 Differential Geometry
Group Theory
Abstract
We show that recent work of Song implies that torsion-free hyperbolic groups with Gromov boundary are realized as fundamental groups of closed 3-manifolds of constant negative curvature if and only if the solution to an associated spherical Plateau problem for group homology is isometric to such a 3-manifold, and suggest some related questions.
Keywords
Cite
@article{arxiv.2207.01720,
title = {Characterizing candidates for Cannon's Conjecture from Geometric Measure Theory},
author = {Tamunonye Cheetham-West and Alexander Nolte},
journal= {arXiv preprint arXiv:2207.01720},
year = {2023}
}
Comments
7 pages. This is the accepted version of the following article: Cheetham-West, T. and Nolte, A. (2023), Characterizing candidates for Cannon's conjecture from geometric measure theory. Bull. London Math. Soc.. https://doi.org/10.1112/blms.12814, which has been published in final form at http://doi.org/10.1112/blms.12814