PreprintCC BY 4.0arXiv
Finite Borel asymptotic dimension of bounded-to-one commutative monoid actions
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 (3r+1−3)/2. This answers a question of Shinko, Weilacher and Yu, and extends a theorem of theirs.
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BibTeX
@misc{wang2026finite,
title = {{Finite Borel asymptotic dimension of bounded-to-one commutative monoid actions}},
author = {Ruijun Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17177},
eprint = {2609.17177},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17177},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Finite Borel asymptotic dimension of bounded-to-one commutative monoid actions
AU - Ruijun Wang
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.17177
UR - https://arxiv.org/abs/2609.17177
AB - 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.
ER -