Open Access
October 2009 Coarse fixed point theorem
Tomohiro Fukaya
Proc. Japan Acad. Ser. A Math. Sci. 85(8): 105-107 (October 2009). DOI: 10.3792/pjaa.85.105


We study group actions on a coarse space and the induced actions on the Higson corona from a dynamical point of view. Our main theorem states that if an action of an abelian group on a proper metric space satisfies certain conditions, the induced action has a fixed point in the Higson corona. As a corollary, we deduce a coarse version of Brouwer’s fixed point theorem.


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Tomohiro Fukaya. "Coarse fixed point theorem." Proc. Japan Acad. Ser. A Math. Sci. 85 (8) 105 - 107, October 2009.


Published: October 2009
First available in Project Euclid: 2 October 2009

zbMATH: 1182.37011
MathSciNet: MR163144
Digital Object Identifier: 10.3792/pjaa.85.105

Primary: 55C20
Secondary: 53C24

Keywords: coarse geometry , fixed point Theorem , Higson corona

Rights: Copyright © 2009 The Japan Academy

Vol.85 • No. 8 • October 2009
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