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A notion of geometric complexity and its application to topological rigidity

- E. Guentner, R. Tessera, Guoliang Yu
- Mathematics
- 4 August 2010

We introduce a geometric invariant, called finite decomposition complexity (FDC), to study topological rigidity of manifolds. We prove for instance that if the fundamental group of a compact… Expand

Amenable hyperbolic groups

- P. Caprace, Yves Cornulier, N. Monod, R. Tessera
- Mathematics
- 16 February 2012

We give a complete characterization of the locally compact groups that are nonelementary Gromov-hyperbolic and amenable. They coincide with the class of mapping tori of discrete or continuous… Expand

Asymptotic isoperimetry on groups and uniform embeddings into Banach spaces

- R. Tessera
- Mathematics
- 6 March 2006

We characterize the possible asymptotic behaviors of the compression associated to a uniform embedding into some Lp-space, with 1 < p < ∞, for a large class of groups including connected Lie groups… Expand

Discrete groups with finite decomposition complexity

- E. Guentner, R. Tessera, Guoliang Yu
- Mathematics
- 7 May 2013

In [GTY] we introduced a geometric invariant, called finite decomposition complexity (FDC), to study topological rigidity of manifolds. In that article we proved the stable Borel conjecture for a… Expand

Metric sparsification and operator norm localization

- Xiaoman Chen, R. Tessera, Xianjin Wang, Guoliang Yu
- Mathematics
- 13 November 2007

Isometric Group Actions on Hilbert Spaces: Growth of Cocycles

- Yves Cornulier, R. Tessera, A. Valette
- Mathematics
- 22 September 2005

Abstract.We study growth of 1-cocycles of locally compact groups, with values in unitary representations. Discussing the existence of 1-cocycles with linear growth, we obtain the following… Expand

Volume of spheres in doubling metric measured spaces and in groups of polynomial growth

- R. Tessera
- Mathematics
- 17 June 2005

(Volume de spheres dans les espaces metriques mesures doublants et dans les groupes a croissance polynomiale) Soit G un groupe localement compact, compactement engendre et U une partie compacte… Expand

Relative expanders

- G. Arzhantseva, R. Tessera
- Mathematics
- 6 February 2014

We exhibit a finitely generated group G and a sequence of finite index normal subgroups such that for every finite generating subset $${S\subseteq G}$$S⊆G, the sequence of finite Cayley graphs (G/Nn,… Expand

Large scale Sobolev inequalities on metric measure spaces and applications

- R. Tessera
- Mathematics
- 25 February 2007

For functions on a metric measure space, we introduce a notion of “gradient at a given scale”. This allows us to define Sobolev inequalities at a given scale. We prove that satisfying a Sobolev… Expand

Admitting a coarse embedding is not preserved under group extensions

- G. Arzhantseva, R. Tessera
- Mathematics
- 4 May 2016

We construct a finitely generated group which is an extension of two finitely generated groups coarsely embeddable into Hilbert space but which itself does not coarsely embed into Hilbert space. Our… Expand

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