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Coarse dynamics and fixed-point theorem

Published online by Cambridge University Press:  11 January 2016

Tomohiro Fukaya*
Affiliation:
Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan, [email protected]
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Abstract

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We study semigroup 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 semigroup on a proper coarse 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.

Keywords

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2011

References

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