Quantitative polynomial cohomology and applications to $\textrm L^p$-measure equivalence
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910017305706496 |
|---|---|
| author | Neumann, Antonio López Paucar, Juan |
| author_facet | Neumann, Antonio López Paucar, Juan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_18463 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantitative polynomial cohomology and applications to $\textrm L^p$-measure equivalence Neumann, Antonio López Paucar, Juan Group Theory Dynamical Systems Metric Geometry 37A20, 20J06, 20F65, 20F18, 57M07, 22E41 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. |
| title | Quantitative polynomial cohomology and applications to $\textrm L^p$-measure equivalence |
| topic | Group Theory Dynamical Systems Metric Geometry 37A20, 20J06, 20F65, 20F18, 57M07, 22E41 |
| url | https://arxiv.org/abs/2512.18463 |