1,312 research outputs found
The L-two cohomology of Artin groups
For each Artin group we compute the reduced ā2-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 ā2-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 defined
by a graph into a graph braid group. The number of strands required
for the braid group is equal to the chromatic number of . 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
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