Catalog · 10.5281/zenodo.23341943
Fixed-exponent boundedness and cocompact permanence in Polish groups
- Martino Lupini · University of Bologna
13 October 2026 · CC BY 4.0 · latest of 2 versions
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Fixed-exponent boundedness and cocompact permanence in Polish groups
Martino Lupini
Abstract
We prove that closed cocompact inclusions and compact normal quotients preserve each fixed open-exhaustion and finite-neighbourhood exponent for Polish groups. The literal open-exhaustion conditions and the finite-neighbourhood conditions have distinct indices, related by an explicit interlacing calculus. We also obtain extension and product bounds. We also give a corrected proof of the previously stated coarse equivalence between a Polish group and a closed cocompact subgroup, using compact transition sets. The final section collects consequences and examples for groups whose coarsely bounded sets are relatively compact.
This paper develops material from the author's monograph Property (OB) and the Coarse Geometry of Polish Groups. It is one of eight separate papers intended to replace the monograph.
GitHub repository: https://github.com/eulogica/property-ob-independent-papers
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- 10.5281/zenodo.23341943
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BibTeX
@unpublished{Lupini202623341943,
title = {Fixed-exponent boundedness and cocompact permanence in Polish groups},
author = {Martino Lupini},
year = {2026},
doi = {10.5281/zenodo.23341943},
note = {Zenodo deposit, latest of 2}
}