On the quasi-isometric rigidity of graphs of surface groups
Group Theory
2023-06-13 v2 Geometric Topology
Abstract
Let be a word hyperbolic group with a cyclic JSJ decomposition that has only rigid vertex groups, which are all fundamental groups of closed surface groups. We show that any group quasi-isometric to is abstractly commensurable with .
Keywords
Cite
@article{arxiv.1904.10482,
title = {On the quasi-isometric rigidity of graphs of surface groups},
author = {Alexander Taam and Nicholas W. M. Touikan},
journal= {arXiv preprint arXiv:1904.10482},
year = {2023}
}
Comments
After some revisions, the referee identified a gap in the proof of Lemma 4.20. The following results are impacted: Corollary 4.28, Corollary 5.19, and Theorem A. The authors believe that Corollary 4.28 may be false. What can be recovered from Sections 5 and 6 is that Churro-Waffle spaces are action rigid. The authors still believe that Theorem A is true and are currently working on another proof