Coarse Homotopy Groups [article]

Paul D. Mitchener
2020 arXiv   pre-print
In 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 cone of 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
more » ... ich we expect to be of relevance also in different contexts.
arXiv:1811.10096v3 fatcat:3rhqvflcpjcnbnixpfr3blmrxm