Lifting coarse homotopies
Abstract
Coarse geometry, and in particular coarse homotopy theory, has proven to be a powerful tool for approaching problems in geometric group theory and higher index theory. In this paper, we continue to develop theory in this area by proving a Coarse Lifting Lemma with respect to a certain class of bornologous surjective maps. This class is wide enough to include quotients by coarsely discontinuous group actions, which allows us to obtain results concerning the coarse fundamental group of quotients which are analogous to classical topological results for the fundamental group. As an application, we compute the fundamental group of metric cones over negatively curved compact Riemannian manifolds.
 Publication:

arXiv eprints
 Pub Date:
 March 2019
 arXiv:
 arXiv:1903.06084
 Bibcode:
 2019arXiv190306084W
 Keywords:

 Mathematics  Geometric Topology;
 Mathematics  Metric Geometry;
 51F99;
 55Q70
 EPrint:
 Considerable edits to improve readability. Proofs are shortened. Everything is done for metric spaces instead of the less wellknown coarse spaces. More intermediate text to guide the reader