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.
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Links and Identifiers
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
Zentralblatt MATH identifier: 05651155
References
T. Fukaya, Coarse dynamics and fixed point property. (Preprint). http://arxiv.org/abs/0812.3475
E. Ghys and P. de la Harpe (eds.), Sur les groupes hyperboliques d'apr$\`e$s Mikhael Gromov, Progress in Mathematics, vol. 83, Birkhäuser Boston, Boston, MA, 1990, Papers from the Swiss Seminar on Hyperbolic Groups held in Bern, 1988.
Mathematical Reviews (MathSciNet): MR1086648
John Roe, Lectures on coarse geometry, University Lecture Series, vol. 31, American Mathematical Society, Providence, RI, 2003.
Mathematical Reviews (MathSciNet): MR2007488
Zentralblatt MATH: 1042.53027
Proceedings of the Japan Academy, Series A, Mathematical Sciences
