Characterizing candidates for Cannon's Conjecture from Geometric Measure Theory

Tamunonye Cheetham-West; Alexander Nolte

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arXiv · 2207.01720

Characterizing candidates for Cannon's Conjecture from Geometric Measure Theory

Tamunonye Cheetham-West·Alexander Nolte

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Abstract

We show that recent work of Song implies that torsion-free hyperbolic groups with Gromov boundary $S^2$ 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.

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BibTeX RIS

Tamunonye Cheetham-West, Alexander Nolte. 2022-07-04. Characterizing candidates for Cannon's Conjecture from Geometric Measure Theory. https://arxiv.org/abs/2207.01720

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