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...

ver descrição completa

Detalhes bibliográficos
Autor: Sequeira Manzino, Emiliano
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
Descrição
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.