Tangent bundles of hyperbolic spaces and proper affine actions on $L^p$ spaces

Indira Chatterji (1) , François Dahmani (2) , Thomas Haettel (3) , Jean Lecureux (4)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
2 IF - Institut Fourier
3 IMAG - Institut Montpelliérain Alexander Grothendieck
4 LMO - Laboratoire de Mathématiques d'Orsay

We define the notion of a negatively curved tangent bundle of a metric measured space. We prove that, when a group $G$ acts on a metric measured space $X$ with a negatively curved tangent bundle, then $G$ acts on some $L^p$ space, and that this action is proper under suitable assumptions. We then check that this result applies to the case when $X$ is a CAT(-1) space or a quasi-tree.

Domaines: Topologie géométrique [math.GT]

Indira Chatterji, François Dahmani, Thomas Haettel, Jean Lecureux. Tangent bundles of hyperbolic spaces and proper affine actions on $L^p$ spaces. 2019. ⟨hal-02006189⟩