Cohomologie $L^p$ en degr\'e 1 des espaces homog\`enes

TL;DR

This paper computes the degree 1 $L^p$-cohomology of Riemannian homogeneous spaces, revealing that non-vanishing reduced cohomology occurs precisely for spaces quasiisometric to negatively curved homogeneous spaces.

Contribution

It provides a complete computation of degree 1 $L^p$-cohomology for Riemannian homogeneous spaces, identifying the conditions for non-vanishing cohomology.

Findings

Reduced cohomology vanishes except for spaces quasiisometric to negatively curved spaces.

Non-vanishing cohomology characterizes negatively curved homogeneous spaces.

The results link geometric properties to cohomological behavior.

Abstract

The $L^p$-cohomology in degree 1 of Riemannian homogeneous spaces is computed. It turns out that reduced cohomology does not vanish exactly for spaces quasiisometric to negatively curved homogeneous spaces.