Relative L^p-cohomology and application to Heintze groups

Emiliano Sequeira

doi:10.54330/afm.142924

Geodesic

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Relative L^p-cohomology and application to Heintze groups

Emiliano Sequeira ¹

¹ Universidad de la República

Annales Fennici Mathematici, Tome 49 (2024) no. 1, p. 23–47.

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Résumé

We introduce the notion of relative $L^p$-cohomology as a quasi-isometry invariant defined for a Gromov-hyperbolic space and a point on its boundary at infinity and reproduce some basic properties of $L^p$-cohomology in this context. In the case of degree 1 we show a relation between the relative and the classical $L^p$-cohomology. As an application, we explicitly construct non-zero relative $L^p$-cohomology classes for a purely real Heintze group of the form $\mathbb{R}^{n-1}\rtimes_\alpha\mathbb{R}$, which gives a way to prove that the eigenvalues of $\alpha$, up to a scalar multiple, are invariant under quasi-isometries.

DOI : 10.54330/afm.142924

Keywords: Heintze groups, quasi-isometry invariant, L^p-cohomolgy, delta-hyperbolicity

Affiliations des auteurs :

Emiliano Sequeira ¹

¹ Universidad de la República

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Emiliano Sequeira. Relative L^p-cohomology and application to Heintze groups. Annales Fennici Mathematici, Tome 49 (2024) no. 1, p. 23–47. doi : 10.54330/afm.142924. http://geodesic.mathdoc.fr/articles/10.54330/afm.142924/

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