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Dismantlability of weakly systolic complexes and applications

Authors: Victor Chepoi and Damian Osajda
Journal: Trans. Amer. Math. Soc. 367 (2015), 1247-1272
MSC (2010): Primary 20F65, 20F67, 05C12, 05C63
Published electronically: October 10, 2014
MathSciNet review: 3280043
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Abstract: The main goal of this paper is proving the fixed point theorem for finite groups acting on weakly systolic complexes. As corollaries we obtain results concerning classifying spaces for the family of finite subgroups of weakly systolic groups and conjugacy classes of finite subgroups. As immediate consequences we get new results on systolic complexes and groups.

The fixed point theorem is proved by using a graph-theoretical tool -- dismantlability. In particular we show that $ 1$-skeleta of weakly systolic complexes, i.e., weakly bridged graphs, are dismantlable. On the way we show numerous characterizations of weakly bridged graphs and weakly systolic complexes.

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Additional Information

Victor Chepoi
Affiliation: Laboratoire d’Informatique Fondamentale, Faculté des Sciences de Luminy, Aix-Marseille Université and CNRS, F-13288 Marseille Cedex 9, France

Damian Osajda
Affiliation: Fakultät für Mathematik, Universität Wien, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria – and – (on leave) Instytut Matematyczny, Uniwersytet Wrocławski, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Received by editor(s): October 11, 2012
Received by editor(s) in revised form: March 23, 2013
Published electronically: October 10, 2014
Additional Notes: The work of the first author was supported in part by the ANR grants OPTICOMB (BLAN06-1-138894) and GGAA (ANR-10-BLAN 0116)
The work of the second author was supported in part by MNiSW grant N201 012 32/0718, MNiSW grant N N201 541738, and by the ANR grants Cannon and Théorie Géométrique des Groupes.
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