99 research outputs found
L^2-Betti numbers of one-relator groups
We determine the L^2-Betti numbers of all one-relator groups and all
surface-plus-one-relation groups (surface-plus-one-relation groups were
introduced by Hempel who called them one-relator surface groups). In particular
we show that for all such groups G, the L^2-Betti numbers b_n^{(2)}(G) are 0
for all n>1. We also obtain some information about the L^2-cohomology of
left-orderable groups, and deduce the non-L^2 result that, in any
left-orderable group of homological dimension one, all two-generator subgroups
are free.Comment: 18 pages, version 3, minor changes. To appear in Math. An
The Farrell-Hsiang method revisited
We present a sufficient condition for groups to satisfy the Farrell-Jones
Conjecture in algebraic K-theory and L-theory. The condition is formulated in
terms of finite quotients of the group in question and is motivated by work of
Farrell-Hsiang.Comment: This version is different from the published version. A number of
typos and an incorrect formula for the transfer before Lemma 6.3 pointed out
by Holger Reich have been correcte
Periods for flat algebraic connections
In previous work, we established a duality between the algebraic de Rham
cohomology of a flat algebraic connection on a smooth quasi-projective surface
over the complex numbers and the rapid decay homology of the dual connection
relying on a conjecture by C. Sabbah, which has been proved recently by T.
Mochizuki for algebraic connections in any dimension. In the present article,
we verify that Mochizuki's results allow to generalize these duality results to
arbitrary dimensions also
Orbit spaces of free involutions on the product of two projective spaces
Let be a finitistic space having the mod 2 cohomology algebra of the
product of two projective spaces. We study free involutions on and
determine the possible mod 2 cohomology algebra of orbit space of any free
involution, using the Leray spectral sequence associated to the Borel fibration
. We also
give an application of our result to show that if has the mod 2 cohomology
algebra of the product of two real projective spaces (respectively complex
projective spaces), then there does not exist any -equivariant
map from for (respectively ), where
is equipped with the antipodal involution.Comment: 14 pages, to appear in Results in Mathematic
Morita Equivalence, Picard Groupoids and Noncommutative Field Theories
In this article we review recent developments on Morita equivalence of star
products and their Picard groups. We point out the relations between
noncommutative field theories and deformed vector bundles which give the Morita
equivalence bimodules.Comment: Latex2e, 10 pages. Conference Proceeding for the Sendai Meeting 2002.
Some typos fixe
Higher algebraic -groups and -split sequences
In this paper, we use -split sequences and derived equivalences
to provide formulas for calculation of higher algebraic -groups (or mod-
-groups) of certain matrix subrings which cover tiled orders, rings related
to chains of Glaz-Vasconcelos ideals, and some other classes of rings. In our
results, we do not assume any homological requirements on rings and ideals
under investigation, and therefore extend sharply many existing results of this
type in the algebraic -theory literature to a more general context.Comment: 20 page
Formality theorems for Hochschild complexes and their applications
We give a popular introduction to formality theorems for Hochschild complexes
and their applications. We review some of the recent results and prove that the
truncated Hochschild cochain complex of a polynomial algebra is non-formal.Comment: Submitted to proceedings of Poisson 200
Yukawa Couplings in Heterotic Compactification
We present a practical, algebraic method for efficiently calculating the
Yukawa couplings of a large class of heterotic compactifications on Calabi-Yau
three-folds with non-standard embeddings. Our methodology covers all of, though
is not restricted to, the recently classified positive monads over favourable
complete intersection Calabi-Yau three-folds. Since the algorithm is based on
manipulating polynomials it can be easily implemented on a computer. This makes
the automated investigation of Yukawa couplings for large classes of smooth
heterotic compactifications a viable possibility.Comment: 38 page
A constructive study of the module structure of rings of partial differential operators
The purpose of this paper is to develop constructive versions of Stafford's theorems on the module structure of Weyl algebras A n (k) (i.e., the rings of partial differential operators with polynomial coefficients) over a base field k of characteristic zero. More generally, based on results of Stafford and Coutinho-Holland, we develop constructive versions of Stafford's theorems for very simple domains D. The algorithmization is based on the fact that certain inhomogeneous quadratic equations admit solutions in a very simple domain. We show how to explicitly compute a unimodular element of a finitely generated left D-module of rank at least two. This result is used to constructively decompose any finitely generated left D-module into a direct sum of a free left D-module and a left D-module of rank at most one. If the latter is torsion-free, then we explicitly show that it is isomorphic to a left ideal of D which can be generated by two elements. Then, we give an algorithm which reduces the number of generators of a finitely presented left D-module with module of relations of rank at least two. In particular, any finitely generated torsion left D-module can be generated by two elements and is the homomorphic image of a projective ideal whose construction is explicitly given. Moreover, a non-torsion but non-free left D-module of rank r can be generated by r+1 elements but no fewer. These results are implemented in the Stafford package for D=A n (k) and their system-theoretical interpretations are given within a D-module approach. Finally, we prove that the above results also hold for the ring of ordinary differential operators with either formal power series or locally convergent power series coefficients and, using a result of Caro-Levcovitz, also for the ring of partial differential operators with coefficients in the field of fractions of the ring of formal power series or of the ring of locally convergent power series. © 2014 Springer Science+Business Media
Latitudinal gradient of nestedness and its potential drivers in stream detritivores
Understanding what mechanisms shape the diversity and composition of biological assemblages across broad-scale gradients is central to ecology. Litter-consuming detritivorous invertebrates in streams show an unusual diversity gradient, with α-diversity increasing towards high latitudes but no trend in γ -diversity. We hypothesized this pattern to be related
to shifts in nestedness and several ecological processes shaping their assemblages (dispersal, environmental filtering and competition). We tested this hypothesis, using a global dataset, by examining latitudinal trends in nestedness and several indicators of the above processes along the latitudinal gradient. Our results suggest that strong environmental filtering and low dispersal in the tropics lead to often species-poor local detritivore assemblages, nested in richer regional assemblages. At higher latitudes, dispersal becomes stronger, disrupting the nested assemblage structure and resulting in local assemblages that are generally more species-rich and non-nested subsets of the regional species pools. Our results provide
evidence that mechanisms underlying assemblage composition and diversity of stream litter-consuming detritivores shift
across latitudes, and provide an explanation for their unusual pattern of increasing α-diversity with latitude. When we repeated these analyses for whole invertebrate assemblages of leaf litter and for abundant taxa showing reverse or no diversity gradients we found no latitudinal patterns, suggesting that function-based rather than taxon-based analyses of assemblages may help elucidate the mechanisms behind diversity gradients
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