Non-hyperbolic automatic groups and groups acting on CAT(0) cube complex
Group Theory
2014-09-25 v1 Geometric Topology
Abstract
We discuss a problem posed by Gersten: Is every automatic group which does not contain Z+Z subgroup, hyperbolic? To study this question, we define the notion of "n-tracks of length n", which is a structure like Z+Z, and prove its existence in the non-hyperbolic automatic groups with mild conditions. As an application, we show that if a group acts effectively, cellularly, properly discontinuously and cocompactly on a CAT(0) cube complex and its quotient is "weakly special", then the above question is answered affirmatively.
Keywords
Cite
@article{arxiv.1309.5553,
title = {Non-hyperbolic automatic groups and groups acting on CAT(0) cube complex},
author = {Yoshiyuki Nakagawa and Makoto Tamura and Yasushi Yamashita},
journal= {arXiv preprint arXiv:1309.5553},
year = {2014}
}
Comments
15 pages, 5 figures