A Degree-Theoretic Proof of a Coarse Fixed Point Principle

Steven Hair

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arXiv · 1008.5131

A Degree-Theoretic Proof of a Coarse Fixed Point Principle

Steven Hair

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Abstract

We introduce a large scale analogue of the classical fixed-point property for continuous maps, which shall apply to coarse maps. We also develop a coarse version of degree for coarse maps on Euclidean spaces. Then, applying a coarse degree-theoretic argument, we prove that every coarse map from a Euclidean half-space to itself has the coarse fixed-point property.

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Steven Hair. 2010-08-30. A Degree-Theoretic Proof of a Coarse Fixed Point Principle. https://arxiv.org/abs/1008.5131

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