Shinko–Weilacher–Yu asymptotic-dimension question
For every finitely generated commutative monoid and every bounded-to-one Borel action , the action has finite Borel asymptotic dimension: .
References
Primary source
Additional references
- Finite Borel asymptotic dimension of bounded-to-one commutative monoid actions — arXiv — Ruijun Wang
Progress summary
An unrefereed preprint claims to settle the question for all bounded-to-one commutative monoid actions, extending the earlier result that required freeness.
The question asks whether every bounded-to-one action of a finitely generated commutative monoid has finite Borel asymptotic dimension.
Known results
- Naryshkin, Shinko, Weilacher, and Yu proved finite Borel asymptotic dimension for free bounded-to-one actions; the corresponding statement without freeness was explicitly left open.
September 15, 2026 claimed resolution
Ruijun Wang's preprint claims the result for all bounded-to-one commutative monoid actions, removing freeness and giving the bound when the group completion has torsion-free rank . The claim is unrefereed and has not been independently verified in the retrieved sources.
Current status (as of September 2026): The free-action case is established, while Ruijun Wang's extension to all bounded-to-one actions is a claimed but unverified resolution.
Solutions 0
No solutions have been posted yet.