# Superrigidité géométrique et applications harmoniques

@inproceedings{Pansu2009SuperrigiditGE, title={Superrigidit{\'e} g{\'e}om{\'e}trique et applications harmoniques}, author={Pierre Pansu}, year={2009} }

These are expanded notes of a course given in Grenoble in june 2004. After a brief description of the harmonic map proof of Margulis' superrigidity and arithmeticity theorems, it is shown how the method might generalize to fundamental groups of simplicial complexes whose links have large enough nonlinear spectral gaps, with emphasis on random groups.

#### 12 Citations

Groups acting on spaces of non-positive curvature

- Mathematics
- 2016

In this survey article, we present some panorama of groups acting on metric spaces of non-positive curvature. We introduce the main examples and their rigidity properties , we show the links between… Expand

On CAT(0) aspects of geometric group theory and some applications to geometric superrigidity

- Mathematics
- 2012

Since their popularization by Gromov in the eighties, CAT(0) metric spaces of bounded curvature as defined by Alexandrov have been the locus of great progress in infinite group theory. Surveying… Expand

Superrigidity in infinite dimension and finite rank via harmonic maps

- Mathematics
- 2012

We prove geometric superrigidity for actions of cocompact lattices in semisimple Lie groups of higher rank on infinite dimensional Riemannian manifolds of nonpositive curvature and finite telescopic… Expand

Un Théorème de Point Fixe sur les Espaces $L^p$

- Mathematics
- 2012

We establish a fixed point theorem for group actions on Lp-spaces, which generalizes a theorem of Zuk and of Ballmann-Swiatkowski to the case p ≠ 2.

Infinite-Dimensional Nonpositively Curved Symmetric Spaces of Finite Rank

- Mathematics
- 2013

This paper concerns a study of three families of non-compact type symmetric spaces of infinite dimension. Although they have infinite dimension they have finite rank. More precisely, we show they… Expand

CAT(0) spaces on which a certain type of singularity is bounded

- Mathematics
- 2010

In this paper, we present a geometric condition for a family of CAT(0) spaces, which ensures that the Izeki-Nayatani invariants of spaces in the family are uniformly bounded from above by a constant… Expand

Torsors, Reductive Group Schemes and Extended Affine Lie Algebras

- Mathematics
- 2011

We give a detailed description of the torsors that correspond to multiloop algebras. These algebras are twisted forms of simple Lie algebras extended over Laurent polynomial rings. They play a… Expand

N ov 2 00 7 Central extensions of groups of sections

- 2009

If q : P → M is a principal K-bundle over the compact manifold M , then any invariant symmetric V-valued bilinear form on the Lie algebra k of K defines a Lie algebra extension of the gauge algebra… Expand

Central extensions of groups of sections

- Mathematics
- 2009

If K is a Lie group and q : P → M is a principal K-bundle over the compact manifold M, then any invariant symmetric V-valued bilinear form on the Lie algebra $${\mathfrak{k}}$$ of K defines a Lie… Expand

Uniform Estimates of Nonlinear Spectral Gaps

- Mathematics, Computer Science
- Graphs Comb.
- 2015

It is shown that nonlinear spectral gaps of a finite connected graph are uniformly bounded from below by a positive constant which is independent of the target metric space. Expand

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