Dismantlability of weakly systolic complexes and applications

Details Dismantlability of weakly systolic complexes and applications Dismantlability of weakly systolic complexes and applications

2009-10-28

arxiv.org/abs/0910.5444v1

Mathematics

Group Theory

Scientific paper

In this paper, we investigate the structural properties of weakly systolic complexes introduced recently by the second author and of their 1-skeletons, the weakly bridged graphs. We present several characterizations of weakly systolic complexes and weakly bridged graphs. Then we prove that weakly bridged graphs are dismantlable. Using this, we establish the fixed point theorem for weakly systolic complexes. As a consequence, we get results about conjugacy classes of finite subgroups and classifying spaces for finite subgroups of weakly systolic groups. As immediate corollaries, we obtain new results on systolic complexes and systolic groups.

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