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.
|Number of pages||3|
|Journal||Proceedings of the Japan Academy Series A: Mathematical Sciences|
|Publication status||Published - 2009|
- Coarse geometry
- Fixed point theorem
- Higson corona
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