Corpus ID: 119563566

Lifting coarse homotopies

  title={Lifting coarse homotopies},
  author={Thomas Weighill},
  journal={arXiv: Geometric Topology},
  • Thomas Weighill
  • Published 2019
  • Mathematics
  • arXiv: Geometric Topology
  • We prove a general lifting lemma for coarse homotopies with respect to a certain class of bornologous surjective maps. This class is wide enough to include quotients by group actions satisfying a coarse discontinuity condition, 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 compact Riemannian manifolds of… CONTINUE READING


    Homotopy Theory with Bornological Coarse Spaces
    • 26
    • PDF
    An alternative definition of coarse structures
    • 26
    Asymptotic topology
    • 61
    • PDF
    Lectures on coarse geometry
    • 533
    • PDF
    The coarse Baum–Connes conjecture for spaces which admit a uniform embedding into Hilbert space
    • 446
    • PDF
    Metric Spaces of Non-Positive Curvature
    • 2,940
    Some categorical aspects of coarse spaces and balleans
    • 19
    Index theory, coarse geometry, and topology of manifolds
    • 228