English

Groups acting on CAT(0) square complexes

Group Theory 2007-05-23 v1 Geometric Topology

Abstract

We study groups acting on CAT(0) square complexes. In particular we show if Y is a nonpositively curved (in the sense of A. D. Alexandrov) finite square complex and the vertex links of Y contain no simple loop consisting of five edges, then any subgroup of the fundamental group of Y either is virtually free abelian or contains a free group of rank two. In addition we discuss when a group generated by two hyperbolic isometries contains a free group of rank two and when two points in the ideal boundary of a CAT(0) 2-complex at Tits distance π\pi apart are the endpoints of a geodesic in the 2-complex.

Keywords

Cite

@article{arxiv.math/0303120,
  title  = {Groups acting on CAT(0) square complexes},
  author = {Xiangdong Xie},
  journal= {arXiv preprint arXiv:math/0303120},
  year   = {2007}
}

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31 pages