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arXiv · 2609.17177

Finite Borel asymptotic dimension of bounded-to-one commutative monoid actions

Ruijun Wang
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Abstract

We prove that every bounded-to-one action of a finitely generated commutative monoid has finite asymptotic dimension, without a freeness assumption. If the group completion has torsion-free rank $r$, we give an explicit upper bound $(3^{r+1}-3)/2$. This answers a question of Shinko, Weilacher and Yu, and extends a theorem of theirs.

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Ruijun Wang. 2026-09-15. Finite Borel asymptotic dimension of bounded-to-one commutative monoid actions. https://arxiv.org/abs/2609.17177

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