$\textrm L^p$ 测度等价下的定量多项式上同调及其应用
群论
2026-02-11 v2 动力系统
度量几何
摘要
我们引入离散群的定量多项式上同调版本，并证明当组合填充函数呈多项式界限时，它与常规群上同调一致。作为应用，我们证明了 nilpotent 群的 Betti 数在互为有界 测度等价下保持不变。我们还利用这一结果获得了关于秩 1 简单 Lie 群中非紧凑格子的新型消失结果。
引用
@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}
}
备注
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!