N ov 2 00 6 UNIFORM INDEPENDENCE IN LINEAR GROUPS

1 6 N ov 2 00 4 Braid Groups and Right Angled Artin Groups Frank Connolly and Margaret Doig

In this article we prove a special case of a conjecture of A. Abrams and R. Ghrist about fundamental groups of certain aspherical spaces. Specifically, we show that the n−point braid group of a linear tree is a right angled Artin group for each n.

1 3 N ov 2 00 1 UNIFORM EXPONENTIAL ERGODICITY OF STOCHASTIC DISSIPATIVE SYSTEMS

We study ergodic properties of stochastic dissipative systems with additive noise. We show that the system is uniformly exponentially ergodic provided the growth of nonlinearity at infinity is faster than linear. The abstract result is applied to the stochastic reaction diffusion equation in R d with d ≤ 3.

N ov 2 00 6 A Combination Theorem for Strong Relative Hyperbolicity Mahan

We prove a combination theorem for trees of (strongly) relatively hyperbolic spaces and finite graphs of (strongly) relatively hyperbolic groups. This gives a geometric extension of Bestvina and Feighn's Combination Theorem for hyperbolic groups.

ar X iv : a st ro - p h / 06 11 09 9 v 1 2 N ov 2 00 6 Nuclear Activity in UZC Compact Groups of Galaxies

ar X iv : m at h / 06 11 35 3 v 2 [ m at h . G N ] 1 6 N ov 2 00 6 SQUARES OF MENGER - BOUNDED GROUPS

Using a portion of the Continuum Hypothesis, we prove that there is a Menger-bounded (also called o-bounded) subgroup of the Baire group Z, whose square is not Menger-bounded. This settles a major open problem concerning boundedness notions for groups, and implies that Menger-bounded groups need not be Scheepers-bounded.