Fundamental groups and descriptive set theory
Abstract
We study the homotopy of loops in a fixed path-connected Polish space from a descriptive set-theoretic viewpoint. We show that many analytic equivalence relations arise this way, and many do not. We also study the “free group” over an equivalence relation.
Fields of Study & Subjects
Homotopy and Cohomology in Algebraic Topology
Mathematics and Applications
Geometric and Algebraic Topology
Publication details
- Journal / source
- Proceedings of the American Mathematical Society
- Volume
- 154
- Issue
- 10
- Pages
- 4477–4488
- Publication date
- 24 April 2026
- Language
- EN