Coarse fixed point theorem
Tomohiro Fukaya
Source: Proc. Japan Acad. Ser. A Math. Sci. Volume 85, Number 8 (2009), 105-107.
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.
Full-text: Open access
Permanent link to this document: http://projecteuclid.org/euclid.pja/1254491213
Digital Object Identifier: doi:10.3792/pjaa.85.105
Mathematical Reviews number (MathSciNet):
MR163144
References
Proceedings of the Japan Academy, Series A, Mathematical Sciences