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Groups acting on CAT(0) square complexes

Xiangdong Xie
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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 $π$ apart are the endpoints of a geodesic in the 2-complex.

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Xiangdong Xie. 2003-03-10. Groups acting on CAT(0) square complexes. https://arxiv.org/abs/math/0303120

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