A sofic group away from amenable groups

We give an example of a sofic group, which is not a limit of amenable groups.Comment: 6 pages, 0 figur

No-splitting property and boundaries of random groups

We prove that random groups in the Gromov density model, at any density, satisfy property (FA), i.e. they do not act non-trivially on trees. This implies that their Gromov boundaries, defined at density less than 1/2, are Menger curves.Comment: 20 page

Conformal dimension and random groups

We give a lower and an upper bound for the conformal dimension of the boundaries of certain small cancellation groups. We apply these bounds to the few relator and density models for random groups. This gives generic bounds of the following form, where $l$ is the relator length, going to infinity. (a) 1 + 1/C < \Cdim(\bdry G) < C l / \log(l), for the few relator model, and (b) 1 + l / (C\log(l)) < \Cdim(\bdry G) < C l, for the density model, at densities $d < 1/16$. In particular, for the density model at densities $d < 1/16$, as the relator length $l$ goes to infinity, the random groups will pass through infinitely many different quasi-isometry classes.Comment: 32 pages, 4 figures. v2: Final version. Main result improved to density < 1/16. Many minor improvements. To appear in GAF

Expansive actions on uniform spaces and surjunctive maps

We present a uniform version of a result of M. Gromov on the surjunctivity of maps commuting with expansive group actions and discuss several applications. We prove in particular that for any group $\Gamma$ and any field \K, the space of $\Gamma$-marked groups $G$ such that the group algebra \K[G] is stably finite is compact.Comment: 21 page

Anosov representations: Domains of discontinuity and applications

The notion of Anosov representations has been introduced by Labourie in his study of the Hitchin component for SL(n,R). Subsequently, Anosov representations have been studied mainly for surface groups, in particular in the context of higher Teichmueller spaces, and for lattices in SO(1,n). In this article we extend the notion of Anosov representations to representations of arbitrary word hyperbolic groups and start the systematic study of their geometric properties. In particular, given an Anosov representation of $\Gamma$ into G we explicitly construct open subsets of compact G-spaces, on which $\Gamma$ acts properly discontinuously and with compact quotient. As a consequence we show that higher Teichmueller spaces parametrize locally homogeneous geometric structures on compact manifolds. We also obtain applications regarding (non-standard) compact Clifford-Klein forms and compactifications of locally symmetric spaces of infinite volume.Comment: 63 pages, accepted for publication in Inventiones Mathematica

Geochemistry of sediments from the Tyrrhenian Sea

At Holes 650A and 651 A, set respectively in the Marsili Basin and the Vavilov Basin, Pleistocene sediments (turbiditic inputs interbedded with essentially hemipelagic sediments) may show layers of mudrocks with moderate to strong induration. Except in the two samples from Hole 651 A, it seems that zeolite crystallization does not play a role in the induration phenomenon. This latter appears to result from in situ clay authigenesis. Secondary K-Fe beidellite or Fe-Mg beidellite form diagenetic growths and bridges between sedimented particles. Turbidites are rich in volcaniclastics (glass, pumices and other volcanogenic elements) but the induration phenomenon appears to be associated essentially with the occurrence of basaltic detritus. It is proposed that clay authigenesis results from low temperature alteration of basaltic fragments issued from Vavilov and probably Marsili seamounts in sediments isolated from seawater by overlying deposits