A Degree-Theoretic Proof of a Coarse Fixed Point Principle

Details A Degree-Theoretic Proof of a Coarse Fixed Point Principle A Degree-Theoretic Proof of a Coarse Fixed Point Principle

2010-08-30

arxiv.org/abs/1008.5131v1

Mathematics

Algebraic Topology

5 pages

Scientific paper

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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