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arXiv · 1309.5553

Non-hyperbolic automatic groups and groups acting on CAT(0) cube complex

Yoshiyuki Nakagawa·Makoto Tamura·Yasushi Yamashita
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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.

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Yoshiyuki Nakagawa, Makoto Tamura, Yasushi Yamashita. 2013-09-22. Non-hyperbolic automatic groups and groups acting on CAT(0) cube complex. https://doi.org/10.1142/s0218196714500349

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