Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-hyperbolic automatic groups and groups acting on CAT(0) cube complex   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.

9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
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The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ex