A Degree-Theoretic Proof of a Coarse Fixed Point Principle

2010/08/30 by Hair, Steven
#Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.1008.5131

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.

Related

• Coarse dynamics and fixed point property
• Fixed-point free maps of Euclidean spaces
• Coarse fixed point properties
• Completely coarse maps are \mathbb R-linear
• Generalisations of coarse spaces