On groups whose actions on finite-dimensional CAT(0) spaces have global fixed points-Reference-Cited by-同舟云学术

On groups whose actions on finite-dimensional CAT(0) spaces have global fixed points

Published:2019-06-13 Issue:6 Volume:22 Page:1089-1099
ISSN:1435-4446
Container-title:Journal of Group Theory
language:en
Short-container-title:

Author:

Kato Motoko¹

Affiliation:

1. Faculty of Science , Ehime University , 2-5 Bunkyocho , Matsuyama , Ehime, 790-0826 , Japan

Abstract

Abstract We give a criterion for group elements to have fixed points with respect to a semi-simple action on a complete CAT(0) space of finite topological dimension. As an application, we show that Thompson’s group T and various generalizations of Thompson’s group V have global fixed points when they act semi-simply on finite-dimensional complete CAT(0) spaces, while it is known that T and V act properly on infinite-dimensional CAT(0) cube complexes.

Funder

Japan Society for the Promotion of Science

Publisher

Walter de Gruyter GmbH

Subject

Algebra and Number Theory

Reference17 articles.

1. M. R. Bridson, On the dimension of CAT(0) spaces where mapping class groups act, J. Reine Angew. Math. 673 (2012), 55–68.

2. M. R. Bridson and A. Haefliger, Metric Spaces of Non-positive Curvature, Grundlehren Math. Wiss. 319, Springer, Berlin, 1999.

3. M. G. Brin, Higher dimensional Thompson groups, Geom. Dedicata 108 (2004), 163–192.

4. K. S. Brown, Finiteness properties of groups, J. Pure Appl. Algebra 44 (1987), no. 1–3, 45–75.

5. J. W. Cannon, W. J. Floyd and W. R. Parry, Introductory notes on Richard Thompson’s groups, Enseign. Math. (2) 42 (1996), no. 3–4, 215–256.

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