English

Fundamental groups and descriptive set theory

Logic 2025-12-03 v1 Algebraic Topology

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.

Keywords

Cite

@article{arxiv.2512.02355,
  title  = {Fundamental groups and descriptive set theory},
  author = {Fanxin Wu},
  journal= {arXiv preprint arXiv:2512.02355},
  year   = {2025}
}
R2 v1 2026-07-01T08:04:57.088Z