Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

Request Permissions   Purchase Content 
 

 

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
DOI: https://doi.org/10.1090/S0002-9947-2014-06137-0
Published electronically: October 10, 2014
MathSciNet review: 3280043
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 20F65, 20F67, 05C12, 05C63

Retrieve articles in all journals with MSC (2010): 20F65, 20F67, 05C12, 05C63


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
Email: dosaj@math.uni.wroc.pl

DOI: https://doi.org/10.1090/S0002-9947-2014-06137-0
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.
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.