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.
- Pub Date:
- March 2019
- Mathematics - Geometric Topology;
- Mathematics - Metric Geometry;
- Considerable edits to improve readability. Proofs are shortened. Everything is done for metric spaces instead of the less well-known coarse spaces. More intermediate text to guide the reader