Dismantlability of weakly systolic complexes and applications
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- by Victor Chepoi and Damian Osajda PDF
- Trans. Amer. Math. Soc. 367 (2015), 1247-1272 Request permission
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
- Email: chepoi@lif.univ-mrs.fr
- 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
- MR Author ID: 813959
- ORCID: 0000-0002-5412-8443
- Email: dosaj@math.uni.wroc.pl
- 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. - © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 367 (2015), 1247-1272
- MSC (2010): Primary 20F65, 20F67, 05C12, 05C63
- DOI: https://doi.org/10.1090/S0002-9947-2014-06137-0
- MathSciNet review: 3280043