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Nagoya Mathematical Journal (1)

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Coarse dynamics and fixed-point theorem
Tomohiro Fukaya
Journal:

Nagoya Mathematical Journal / Volume 202 / June 2011

Published online by Cambridge University Press:

11 January 2016, pp. 1-13

Print publication:

June 2011
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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.