Quantitative polynomial cohomology and applications to \textrm L^p-measure equivalence

2025/12/20 by Antonio López Neumann, Neumann, Antonio López, Juan Paucar +1
Mathematics · #Geometry and complex manifolds #Advanced Operator Algebra Research #Geometric and Algebraic Topology

paper · doi:10.48550/arxiv.2512.18463

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 \textrm L^p-measure equivalence. We also use this to obtain new vanishing results for non-cocompact lattices in rank 1 simple Lie groups.

Citations

• L^p measure equivalence of nilpotent groups
• On the stability of hyperbolicity under quantitative measure equivalence
• On the Dehn functions of central products of nilpotent groups
• Higher Kazhdan property and unitary cohomology of arithmetic groups
• Non-vanishing for group L^p-cohomology of solvable and semisimple Lie groups
• Homological Dehn functions of groups of type FP₂
• Quantitative measure equivalence between amenable groups
• Cohomological induction and uniform measure equivalence
• Invariance of non-vanishing of first l^p-cohomology under L^q-Measured Equivalence
• Filling functions of arithmetic groups
• Filling Invariants of Stratified Nilpotent Lie Groups
• Optimal higher-dimensional Dehn functions for some CAT(0) lattices
• Integrable measure equivalence and rigidity of hyperbolic lattices
• A short proof of Gromov's filling inequality
• Homological Invariants and Quasi-Isometry

Related

• L^p measure equivalence of nilpotent groups
• Invariance of non-vanishing of first l^p-cohomology under L^q-Measured Equivalence
• Non-vanishing for group L^p-cohomology of solvable and semisimple Lie groups
• Well-distribution of Polynomial maps on locally compact groups
• Quantitative Polynomial Wiener-Wintner Theorems