De Rham $L^p$-Cohomology For Higher Rank Spaces And Groups: Critical Exponents And Rigidity
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866914235235172352 |
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| author | Bourdon, Marc Rémy, Bertrand |
| author_facet | Bourdon, Marc Rémy, Bertrand |
| contents | We initiate the investigation of critical exponents (in degree equal to the rank) for the vanishing of L^p-cohomology of higher rank Lie groups and related manifolds. We deal with the rank 2 case and exhibit such phenomena for SL$_3$(R) and for a family of 5-dimensional solvable Lie groups. This leads us to exhibit a continuum of quasi-isometry classes of rank 2 solvable Lie groups of non-positive curvature. We provide a detailed description of the $L^p$-cohomology of the real and complex hyperbolic spaces, to be combined with a spectral sequence argument for our higher-rank results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_14025 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | De Rham $L^p$-Cohomology For Higher Rank Spaces And Groups: Critical Exponents And Rigidity Bourdon, Marc Rémy, Bertrand Group Theory Differential Geometry 20J05, 20J06, 22E15, 22E41, 53C35, 55B35, 57T10, 57T15 We initiate the investigation of critical exponents (in degree equal to the rank) for the vanishing of L^p-cohomology of higher rank Lie groups and related manifolds. We deal with the rank 2 case and exhibit such phenomena for SL$_3$(R) and for a family of 5-dimensional solvable Lie groups. This leads us to exhibit a continuum of quasi-isometry classes of rank 2 solvable Lie groups of non-positive curvature. We provide a detailed description of the $L^p$-cohomology of the real and complex hyperbolic spaces, to be combined with a spectral sequence argument for our higher-rank results. |
| title | De Rham $L^p$-Cohomology For Higher Rank Spaces And Groups: Critical Exponents And Rigidity |
| topic | Group Theory Differential Geometry 20J05, 20J06, 22E15, 22E41, 53C35, 55B35, 57T10, 57T15 |
| url | https://arxiv.org/abs/2312.14025 |