Fundamental groups and descriptive set theory

Fanxin Wu

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arXiv · 2512.02355

Fundamental groups and descriptive set theory

Fanxin Wu

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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.

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Fanxin Wu. 2025-12-02. Fundamental groups and descriptive set theory. https://arxiv.org/abs/2512.02355

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