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.
Publié le : 2009-10-15
Classification:
Coarse geometry,
Higson corona,
fixed point theorem,
55C20,
53C24
@article{1254491213,
author = {Fukaya, Tomohiro},
title = {Coarse fixed point theorem},
journal = {Proc. Japan Acad. Ser. A Math. Sci.},
volume = {85},
number = {2},
year = {2009},
pages = { 105-107},
language = {en},
url = {http://dml.mathdoc.fr/item/1254491213}
}
Fukaya, Tomohiro. Coarse fixed point theorem. Proc. Japan Acad. Ser. A Math. Sci., Tome 85 (2009) no. 2, pp. 105-107. http://gdmltest.u-ga.fr/item/1254491213/