Relative L^p-cohomology and application to Heintze groups
We introduce the notion ofrelativeLp-cohomologyas a quasi-isometry invariantdefined for a Gromov-hyperbolic space and a point on its boundary at infinity and reproduce somebasic properties ofLp-cohomology in this context. In the case of degree1we show a relation betweenthe relative and the classical...
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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2024 |
| País: | Uruguay |
| Recursos: | Universidad de la República |
| Repositorio: | COLIBRI |
| Idioma: | inglés |
| OAI Identifier: | oai:colibri.udelar.edu.uy:20.500.12008/48520 |
| Acesso em linha: | https://hdl.handle.net/20.500.12008/48520 |
| Access Level: | acceso abierto |
| Palavra-chave: | HEINTZE GROUPS QUASI-ISOMETRY INVARIANT L^P-COHOMOLGY DELTA-HYPERBOLICITY |
| Resumo: | We introduce the notion ofrelativeLp-cohomologyas a quasi-isometry invariantdefined for a Gromov-hyperbolic space and a point on its boundary at infinity and reproduce somebasic properties ofLp-cohomology in this context. In the case of degree1we show a relation betweenthe relative and the classicalLp-cohomology. As an application, we explicitly construct non-zerorelativeLp-cohomology classes for a purely real Heintze group of the formRn−1⋊αR, which gives away to prove that the eigenvalues ofα, up to a scalar multiple, are invariant under quasi-isometries. |
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