Coarse Homotopy Groups
Geometric Topology
2023-08-14 v3 Algebraic Topology
Abstract
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 which we expect to be of relevance also in different contexts.
Cite
@article{arxiv.1811.10096,
title = {Coarse Homotopy Groups},
author = {Paul D. Mitchener and Behnam Norouzizadeh and Thomas Schick},
journal= {arXiv preprint arXiv:1811.10096},
year = {2023}
}
Comments
26 pages. v3: few typos corrected. Version to appear in Mathematische Nachrichten