Bowditch showed that a one-ended hyperbolic group which is not a triangle group splits over a two-ended group if and only if its boundary has a local cut point. As a corollary one obtains that splittings of hyperbolic groups over twoended groups are preserved under quasi-isometries. In this note we give a more direct proof of this corollary.

We consider splittings of groups over finite and two-ended subgroups. We study the combinatorics of such splittings using generalisations of Whitehead graphs. In the case of hyperbolic groups, we relate this to the topology of the boundary. In particular, we give a proof that the boundary of a one-ended strongly accessible hyperbolic group has no global cut point. AMS Classification 20F32

We review the recent proposal that the most fascinating brain properties are related to the fact that it always stays close to a second order phase transition. In such conditions, the collective of neuronal groups can reliably generate robust and flexible behavior, because it is known that at the critical point there is the largest abundance of metastable states to choose from. Here we review t...

We prove that the Dirichlet fundamental polyhedron for a cyclic group generated by a unipotent or hyperbolic element y acting on complex hyperbolic «-space centered at an arbitrary point w is bounded by the two hypersurfaces equidistant from the pairs w, yw and w,y~lw respectively. The proof relies on a convexity property of the distance to an isometric flow containing y.

We study electric, thermal, and thermoelectric conductivities in the vicinity of a z = 2 superconductor-diffusive metal transition in two dimensions, both in the high and low frequency limits. We find violation of the Wiedemann-Franz law and a dc thermoelectric conductivity α that does not vanish at low temperatures, in contrast to Fermi liquids. We introduce a Langevin equation formalism to st...

In the previous paper, Robert Riley [4] and his computer file Poincaré found a fundamental domain for the action of a discrete group G of isometries of hyperbolic space H3 generated by three parabolics. In this paper, we show that the orbit space H3/G is homeomorphic to a complement 53 — k*, where k* is k union a point and where k is the (3,3,3) pretzel knot. Furthermore, HI 3/G is equipped wit...

The use of statistical fluctuations as probes of the microscopic dynamics of hot and dense hadronic matter is reviewed. Critical fluctuations near the critical point of QCD matter are predicted to enhance fluctuations in pionic observables. Chemical fluctuations, especially those of locally conserved quantum numbers, such as electric charge and baryon number, can probe the nature of the carrier...

016405-1 We consider a two-dimensional itinerant antiferromagnet near a quantum-critical point. We show that, contrary to conventional wisdom, fermionic excitations in the ordered state are not the usual Fermi-liquid quasiparticles. Instead, down to very low frequencies, the fermionic self-energy varies as !2=3. This non-Fermi-liquid behavior originates in the coupling of fermions to the longit...

We describe some of the recent results obtained for models with absorbing states. First, we present the nonequilibrium absorbing-state Potts model and discuss some of the factors that might affect the critical behaviour of such models. In particular we show that in two dimensions the further neighbour interactions might split the voter critical point into two critical points. We also describe s...

We call Poincaré time the time associated to the Poincaré (or first return) map of a vector field. In this paper we prove the non-accumulation of isolated critical points of the Poincaré time T on hyperbolic polycycles of polynomial vector fields. The result is obtained by proving that the Poincaré time of a hyperbolic polycycle either has an unbounded principal part or is an almost regular fun...