Relative L^p-cohomology and application to Heintze groups

Kirjoittajat

  • Emiliano Sequeira Universidad de la República

Avainsanat:

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

Abstrakti

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.

 

Osasto
Articles

Julkaistu

2024-01-31

Viittaaminen

Sequeira, E. (2024). Relative L^p-cohomology and application to Heintze groups. Annales Fennici Mathematici, 49(1), 23–47. https://doi.org/10.54330/afm.142924