The L-two cohomology of Artin groups

For each Artin group we compute the reduced ℓ2-cohomology of its 'Salvetti complex'. This is a CW-complex which is conjectured to be a model for the classifying space of the Artin group. When this conjecture is known to hold our calculation describes the ℓ2-cohomology of the Artin group

The strong Atiyah conjecture for right-angled Artin and Coxeter groups

We prove the strong Atiyah conjecture for right-angled Artin groups and right-angled Coxeter groups. More generally, we prove it for groups which are certain finite extensions or elementary amenable extensions of such groups.Comment: Minor change

A conserved metalloprotease mediates ecdysis in Caenorhabditis elegans

Molting is required for progression between larval stages in the life cycle of nematodes. We have identified four mutant alleles of a <i>Caenorhabditis elegans</i> metalloprotease gene, <i>nas-37</i>, that cause incomplete ecdysis. At each molt the cuticle fails to open sufficiently at the anterior end and the partially shed cuticle is dragged behind the animal. The gene is expressed in hypodermal cells 4 hours before ecdysis during all larval stages. The <i>NAS-37</i> protein accumulates in the anterior cuticle and is shed in the cuticle after ecdysis. This pattern of protein accumulation places NAS- 37 in the right place and at the right time to degrade the cuticle to facilitate ecdysis. The nas-37 gene has orthologs in other nematode species, including parasitic nematodes, and they undergo a similar shedding process. For example, <i>Haemonchus contortus</i> molts by digesting a ring of cuticle at the tip of the nose. Incubating <i>Haemonchus</i> larvae in extracted exsheathing fluids causes a refractile ring of digested cuticle to form at the tip of the nose. When <i>Haemonchus</i> cuticles are incubated with purified NAS-37, a similar refractile ring forms. NAS-37 degradation of the <i>Haemonchus</i> cuticle suggests that the metalloproteases and the cuticle substrates involved in exsheathment of parasitic nematodes are conserved in free-living nematodes

Colorings of simplicial complexes and vector bundles over Davis-Januszkiewicz spaces

We show that coloring properties of a simplicial complex K are reflected by splitting properties of a bundle over the associated Davis-Januszkiewicz space whose Chern classes are given by the elementary symmetric polynomials in the generators of the Stanley-Reisner algebra of K.Comment: 8 page

Embedding right-angled Artin groups into graph braid groups

We construct an embedding of any right-angled Artin group $G(\Delta)$ defined by a graph $\Delta$ into a graph braid group. The number of strands required for the braid group is equal to the chromatic number of $\Delta$. This construction yields an example of a hyperbolic surface subgroup embedded in a two strand planar graph braid group.Comment: 8 pages. Final version, appears in Geometriae Dedicata

Odd-dimensional Charney-Davis conjecture

More than once we have heard that the Charney-Davis Conjecture makes sense only for odd-dimensional spheres. This is to point out that in fact it is also a statement about even-dimensional spheres.Comment: 3 pages, no figure

Exotic torus manifolds and equivariant smooth structures on quasitoric manifolds

In 2006 Masuda and Suh asked if two compact non-singular toric varieties having isomorphic cohomology rings are homeomorphic. In the first part of this paper we discuss this question for topological generalizations of toric varieties, so-called torus manifolds. For example we show that there are homotopy equivalent torus manifolds which are not homeomorphic. Moreover, we characterize those groups which appear as the fundamental groups of locally standard torus manifolds. In the second part we give a classification of quasitoric manifolds and certain six-dimensional torus manifolds up to equivariant diffeomorphism. In the third part we enumerate the number of conjugacy classes of tori in the diffeomorphism group of torus manifolds. For torus manifolds of dimension greater than six there are always infinitely many conjugacy classes. We give examples which show that this does not hold for six-dimensional torus manifolds.Comment: 21 pages, 2 figures, results about quasitoric manifolds adde

A pearl on SAT solving in Prolog

A succinct SAT solver is presented that exploits the control provided by delay declarations to implement watched literals and unit propagation. Despite its brevity the solver is surprisingly powerful and its elegant use of Prolog constructs is presented as a programming pearl

High frequency sound in superfluid 3He-B

We present measurements of the absolute phase velocity of transverse and longitudinal sound in superfluid 3He-B at low temperature, extending from the imaginary squashing mode to near pair-breaking. Changes in the transverse phase velocity near pair-breaking have been explained in terms of an order parameter collective mode that arises from f-wave pairing interactions, the so-called J=4- mode. Using these measurements, we establish lower bounds on the energy gap in the B-phase. Measurement of attenuation of longitudinal sound at low temperature and energies far above the pair-breaking threshold, are in agreement with the lower bounds set on pair-breaking. Finally, we discuss our estimations for the strength of the f-wave pairing interactions and the Fermi liquid parameter, F4s.Comment: 15 pages, 8 figures, accepted to J. Low Temp. Phy

Condensate Heating by Atomic Losses

Atomic Bose-Einstein condensate is heated by atomic losses. Predicted depletion ranges from 1% for a uniform 3D condensate to around 10% for a quasi-1D condensate in a harmonic trap.Comment: 4 pages in RevTex, 1 eps figur