478,325 research outputs found
Cohomology of Coxeter groups with group ring coefficients: II
For any Coxeter group W, we define a filtration of H^*(W;ZW) by W-submodules
and then compute the associated graded terms. More generally, if U is a CW
complex on which W acts as a reflection group we compute the associated graded
terms for H_*(U) and, in the case where the action is proper and cocompact, for
H^*_c(U).Comment: This is the version published by Algebraic & Geometric Topology on 15
September 200
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Echoes of the sea around us—Human hopes in the balance
Earth’s human life-support system shows signs of failing. Human capacity to alter landscapes and the atmosphere is reaching catastrophic levels. Only the oceans seemed to be beyond control, but still they are not beyond human influence. Limited experience in protecting nature’s integrity, health, and resilience in seascapes offers the potential to reverse sliding global environmental conditions by providing realistic expectations, offering moral fortitude, stimulating imagination, and proffering hope. The ocean’s capacity to evoke human awe and inspiration may be sufficient to focusmankind on the global existential threats we face. It is now vital to heed Rachael Carson’s 1937 prescient observation “Against this cosmic background the lifetime of a particular plant or animal appears not as a drama complete in itself but only as a brief interlude in a panorama of endless change.” The world will keep spinning, whether people are able to enjoy the ride or not
Coefficients in powers of the log series
We determine the p-exponent in many of the coefficients in the power series
(log(1+x)/x)^t, where t is any integer. In our proof, we introduce a variant of
multinomial coefficients. We also characterize the power series x/log(1+x) by
certain zero coefficients in its powers.Comment: 8 page
Weighted -cohomology of Coxeter groups
Given a Coxeter system and a positive real multiparameter \bq, we
study the "weighted -cohomology groups," of a certain simplicial complex
associated to . These cohomology groups are Hilbert spaces, as
well as modules over the Hecke algebra associated to and the
multiparameter . They have a "von Neumann dimension" with respect to the
associated "Hecke - von Neumann algebra," . The dimension of the
cohomology group is denoted . It is a nonnegative real number
which varies continuously with . When is integral, the
are the usual -Betti numbers of buildings of type and thickness
. For a certain range of , we calculate these cohomology groups as
modules over and obtain explicit formulas for the . The
range of for which our calculations are valid depends on the region of
convergence of the growth series of . Within this range, we also prove a
Decomposition Theorem for , analogous to a theorem of L. Solomon on the
decomposition of the group algebra of a finite Coxeter group.Comment: minor change
The -homology of even Coxeter groups
Given a Coxeter system (W,S), there is an associated CW-complex, Sigma, on
which W acts properly and cocompactly. We prove that when the nerve L of (W,S)
is a flag triangulation of the 3-sphere, then the reduced -homology of
Sigma vanishes in all but the middle dimension.Comment: 15 pages, 1 figur
On asymptotic dimension of groups
We prove a version of the countable union theorem for asymptotic dimension
and we apply it to groups acting on asymptotically finite dimensional metric
spaces. As a consequence we obtain the following finite dimensionality
theorems. A) An amalgamated product of asymptotically finite dimensional groups
has finite asymptotic dimension: asdim A *_C B < infinity. B) Suppose that G'
is an HNN extension of a group G with asdim G < infinity. Then asdim G'<
infinity. C) Suppose that \Gamma is Davis' group constructed from a group \pi
with asdim\pi < infinity. Then asdim\Gamma < infinity.Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol1/agt-1-4.abs.htm
Cosmic D-Strings and Vortons in Supergravity
Recent developments in string inspired models of inflation suggest that
D-strings are formed at the end of inflation. Within the supergravity model of
D-strings there are 2(n-1) chiral fermion zero modes for a D-string of winding
n. Using the bounds on the relic vorton density, we show that D-strings with
winding number n>1 are more strongly constrained than cosmic strings arising in
cosmological phase transitions. The D-string tension of such vortons, if they
survive until the present, has to satisfy 8\pi G_N \mu \lesssim p 10^{-26}
where p is the intercommutation probability. Similarly, D-strings coupled with
spectator fermions carry currents and also need to respect the above bound.
D-strings with n=1 do not carry currents and evade the bound. We discuss the
coupling of D-strings to supersymmetry breaking. When a single U(1) gauge group
is present, we show that there is an incompatibility between spontaneous
supersymmetry breaking and cosmic D-strings. We propose an alternative
mechanism for supersymmetry breaking, which includes an additional U(1), and
might alleviate the problem. We conjecture what effect this would have on the
fermion zero modes.Comment: 11 page
Distributional Analyses of Revenue Options for Alaska
A new report commissioned by Rasmuson Foundation as part of its Plan4Alaska campaign finds that while strategies currently proposed to close Alaska's 100,000 (or over $200,000 for married couples)
What Inspires Leisure Time Invention?
This paper seeks to understand the intriguing but only sparsely explored phenomenon of “leisure time invention,” where the main underlying idea for the new product or process occurs when the inventor is away from the workplace. We add to previous research by focussing on the inventive creativity of the individual researcher, and reassessing the image of researchers inventing during unpaid time – who have often been dispatched as “hobbyists”. Based on the responses from a survey of over 3,000 German inventors, we tested hypotheses on the conditions under which leisure time invention is likely to arise. Results suggest that the incidence of leisure time invention is positively related to exposure to a variety of knowledge inputs – but, surprisingly, not to the quality of prior inventive output. Leisure time inventions are more frequently observed in conceptual-based technologies than in science-based technologies, in smaller R&D projects, and in externally financed R&D projects
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