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.
"Coarse fixed point theorem." Proc. Japan Acad. Ser. A Math. Sci. 85 (8) 105 - 107, October 2009. https://doi.org/10.3792/pjaa.85.105