Hostname: page-component-5c6d5d7d68-wbk2r Total loading time: 0 Render date: 2024-08-27T12:59:14.867Z Has data issue: false hasContentIssue false
  • English
  • Français

The fixed point theorem for simplicial nonpositive curvature

Published online by Cambridge University Press:  01 May 2008

PIOTR PRZYTYCKI
PIOTR PRZYTYCKI*
Affiliation:
Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-956 Warsaw, Poland. e-mail: pprzytyc@mimuw.edu.pl
Get access Rights & Permissions [Opens in a new window]

Abstract

We prove that for an action of a finite group G on a systolic complex X there exists a G–invariant subcomplex of X of diameter ≤5. For 7–systolic locally finite complexes we prove there is a fixed point for the action of any finite G. This implies that free products with amalgamation (and HNN extensions) of 7–systolic groups over finite subgroups are also 7–systolic.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 144 , Issue 3 , May 2008 , pp. 683 - 695
Copyright
Copyright © Cambridge Philosophical Society 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Bridson, M. and Haefliger, A.. Metric Spaces of Non-Positive Curvature. Grundlehren der mathematischen Wissenschaften 319 (Springer, 1999).Google Scholar
[2]Elsner, T.. Flats and flat torus theorem in systolic spaces. Submitted.Google Scholar
[3]Haglund, F.. Complexes simpliciaux hyperboliques de grande dimension. Preprint (Prepublication Orsay 71, 2003).Google Scholar
[4]Haglund, F. and Światkowski, J.. Separating quasi–convex subgroups in 7–systolic groups. Groups, Geometry and Dynamics, to appear.Google Scholar
[5]Osajda, D.. Ideal boundary of 7–systolic complexes and groups. Submitted.Google Scholar
[6]Januszkiewicz, T. and ÁSwimudahua, J.tkowski. Simplicial nonpositive curvature. Publ. Maths. Inst. Hanks Etudes Sci., 104 (1) (2006), 1–85.CrossRefGoogle Scholar
[7]Januszkiewicz, T. and ÁSwimudahua, J.tkowski. Filling invariants of systolic complexes and groups. Geom. Topol. 11 (2007), 727–758.CrossRefGoogle Scholar
[8]Scott, P. and Wall, T.. Topological methods in group theory. In Homological Group Theory. London Math. Soc. Lecture Notes Ser. 36 (1979), 137–214.CrossRefGoogle Scholar