Quantitative polynomial cohomology and applications to $\textrm L^p$-measure equivalence
Group Theory
2026-02-11 v2 Dynamical Systems
Metric Geometry
Abstract
We introduce a quantitative version of polynomial cohomology for discrete groups and show that it coincides with usual group cohomology when combinatorial filling functions are polynomially bounded. As an application, we show that Betti numbers of nilpotent groups are invariant by mutually cobounded -measure equivalence. We also use this to obtain new vanishing results for non-cocompact lattices in rank 1 simple Lie groups.
Keywords
Cite
@article{arxiv.2512.18463,
title = {Quantitative polynomial cohomology and applications to $\textrm L^p$-measure equivalence},
author = {Antonio López Neumann and Juan Paucar},
journal= {arXiv preprint arXiv:2512.18463},
year = {2026}
}
Comments
43 pages. This is v2. We improved presentation and added new consequences in Section 5. Namely, Francesco Fournier-Facio and Roman Sauer pointed out that our methods could show that non-uniform octonionic lattices inherit property [T_3] from the ambient Lie group F_4^{-20}. Comments are welcome!