2003/03/10 by Xiangdong Xie, Xie, Xiangdong
Mathematics · #20E07 #20F67 #57M20 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #math.GR #math.GT #msc:20E07 #msc:20F67 #msc:57M20
paper · pdf · doi:10.48550/arxiv.math/0303120
31 pages
arxiv created 2003/03/10 · arxiv updated 2009/11/30
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.