Relative L^p-cohomology and application to Heintze groups
Annales Fennici Mathematici, Tome 49 (2024) no. 1, p. 23–47
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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.
Keywords:
Heintze groups, quasi-isometry invariant, L^p-cohomolgy, delta-hyperbolicity
Affiliations des auteurs :
Emiliano Sequeira 1
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
@article{AFM_2024_49_1_a1,
author = {Emiliano Sequeira},
title = {Relative {L^p-cohomology} and application to {Heintze} groups},
journal = {Annales Fennici Mathematici},
pages = {23{\textendash}47--23{\textendash}47},
year = {2024},
volume = {49},
number = {1},
doi = {10.54330/afm.142924},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.54330/afm.142924/}
}
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