Homotopy types of fine curve and fine arc complexes
Abstract
The fine curve complex of a surface is a simplicial complex whose vertices are essential simple closed curves and whose $k$-simplices are collections of $k+1$ disjoint curves. We prove that the fine curve complex is homotopy equivalent to the curve complex. We also prove that the fine arc complex is contractible.
Fields of Study & Subjects
Geometric and Algebraic Topology
Geometric Analysis and Curvature Flows
Homotopy and Cohomology in Algebraic Topology
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 10 February 2026
- Language
- EN
- Document type
- Preprint