Coarse homotopy groups
Copyright policy )Coarse homotopy groups
AbstractIn this note on coarse geometry we revisit coarse homotopy. We prove that coarse homotopy indeed is an equivalence relation, and this in the most general context of abstract coarse structures. We introduce (in a geometric way) coarse homotopy groups. The main result is that the coarse homotopy groups of a cone over a compact simplicial complex coincide with the usual homotopy groups of the underlying compact simplicial complex. To prove this we develop geometric triangulation techniques for cones which we expect to be of relevance also in different contexts.
- University of Göttingen Germany
- White Rose Consortium: University of Leeds; University of Sheffield; University of York United Kingdom
- University of Sheffield United Kingdom
Lipschitz and coarse geometry of metric spaces, Geometric Topology (math.GT), coarse algebraic topology, simplicial geometry, Mathematics - Geometric Topology, homotopy groups, Homotopy groups, general; sets of homotopy classes, FOS: Mathematics, Algebraic Topology (math.AT), Mathematics - Algebraic Topology, coarse geometry, geometric triangulations
Lipschitz and coarse geometry of metric spaces, Geometric Topology (math.GT), coarse algebraic topology, simplicial geometry, Mathematics - Geometric Topology, homotopy groups, Homotopy groups, general; sets of homotopy classes, FOS: Mathematics, Algebraic Topology (math.AT), Mathematics - Algebraic Topology, coarse geometry, geometric triangulations
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