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arXiv · 2603.29524

Geometric Inverse Semigroup Theory: a note on the Milnor-Schwarz Lemma for inverse monoids

Giorgio Mangioni·Francesco Tesolin
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Abstract

We generalise the Milnor-Schwarz lemma to inverse monoids acting on presheaves of geodesic metric spaces. We provide two proofs of this fact: one only uses elementary techniques, inspired by the arguments for group actions on metric spaces; the other involves a version of the Vietoris-Rips complex, and builds on work of Chung-Mart\'inez-Szak\'acs.

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BibTeXRIS

Giorgio Mangioni, Francesco Tesolin. 2026-03-31. Geometric Inverse Semigroup Theory: a note on the Milnor-Schwarz Lemma for inverse monoids. https://doi.org/10.1112/blms.70482

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