Vanishing of the first reduced cohomology with values in an $L^p$-representation
| dc.creator | Tessera, Romain | |
| dc.date | 2006-10-31 | |
| dc.date | 2007-06-28 | |
| dc.date.accessioned | 2026-07-07T08:12:47Z | |
| dc.date.available | 2026-07-07T08:12:47Z | |
| dc.description | We prove that the first reduced cohomology with values in a mixing Lp-representation, p larger than 1, vanishes for a class of amenable groups including connected amenable Lie groups. In particular this solves for this class of amenable groups a conjecture of Gromov saying that every finitely generated amenable group has no first reduced lp-cohomology. As a byproduct, we prove a conjecture by Pansu. Namely, the first reduced Lp-cohomology on homogeneous, closed at infinity, Riemannian manifolds vanishes. We also prove that a Gromov hyperbolic geodesic metric measure space with bounded geometry admitting a bi-Lipschitz embedded 3-regular tree has non-trivial first reduced Lp-cohomology for large enough p. Combining our results with those of Pansu, we characterize Gromov hyperbolic homogeneous manifolds: these are the ones having non-zero first reduced Lp-cohomology for some p larger than 1. | |
| dc.description | 20 pages, correction: minor changes (introduction), corrections: we improved the redaction (in particular, adding more details to the proofs), and showed a more general statement for hyperbolic spaces | |
| dc.identifier | https://arxiv.org/abs/math/0611001 | |
| dc.identifier | http://arxiv.org/abs/math/0611001 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/132576 | |
| dc.subject | Geometric Topology | |
| dc.subject | Group Theory | |
| dc.subject | 20F65; 22F30 | |
| dc.title | Vanishing of the first reduced cohomology with values in an $L^p$-representation | |
| dc.type | text |