Coarse fixed point theorem

Tomohiro Fukaya

doi:10.3792/pjaa.85.105

Coarse fixed point theorem

Tomohiro Fukaya

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	105-107
Number of pages	3
Journal	Proceedings of the Japan Academy Series A: Mathematical Sciences
Volume	85
Issue number	8
DOIs	https://doi.org/10.3792/pjaa.85.105
Publication status	Published - 2009
Externally published	Yes

Keywords

Coarse geometry
Fixed point theorem
Higson corona

ASJC Scopus subject areas

Mathematics(all)

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10.3792/pjaa.85.105

Cite this

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abstract = "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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AB - 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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KW - Fixed point theorem

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Coarse fixed point theorem

Abstract

Keywords

ASJC Scopus subject areas

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