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Random groups have fixed points on $ \mathrm{CAT}(0)$ cube complexes

Authors: Koji Fujiwara and Tetsu Toyoda
Journal: Proc. Amer. Math. Soc. 140 (2012), 1023-1031
MSC (2010): Primary 53C23; Secondary 20F65, 20P05, 51F99
Published electronically: October 4, 2011
MathSciNet review: 2869086
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Abstract: We prove that a random group has fixed points when it isometrically acts on a $ \textrm {CAT}(0)$ cube complex. We do not assume that the action is simplicial.

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Additional Information

Koji Fujiwara
Affiliation: Graduate School of Information Science, Tohoku University, Aoba-ku, Sendai, Miyagi, 980-8579, Japan

Tetsu Toyoda
Affiliation: Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya, 464-8602, Japan

Received by editor(s): December 17, 2010
Received by editor(s) in revised form: December 19, 2010
Published electronically: October 4, 2011
Additional Notes: The first author is supported by Grant-in-Aid for Scientific Research (No. 19340013).
Communicated by: Ken Ono
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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