170 research outputs found
Splitting of Gysin extensions
Let X --> B be an orientable sphere bundle. Its Gysin sequence exhibits
H^*(X) as an extension of H^*(B)-modules. We prove that the class of this
extension is the image of a canonical class that we define in the Hochschild
3-cohomology of H^*(B), corresponding to a component of its A_infty-structure,
and generalizing the Massey triple product. We identify two cases where this
class vanishes, so that the Gysin extension is split. The first, with rational
coefficients, is that where B is a formal space; the second, with integer
coefficients, is where B is a torus.Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol1/agt-1-37.abs.htm
Hermitian K-theory of the integers
The 2-primary torsion of the higher algebraic K-theory of the integers has
been computed by Rognes and Weibel. In this paper we prove analogous results
for the Hermitian K-theory of the integers with 2 inverted (denoted by Z'). We
also prove in this case the analog of the Lichtenbaum conjecture for the
hermitian K-theory of Z' : the homotopy fixed point set of a suitable Z/2
action on the classifying space of the algebraic K-theory of Z' is the
hermitian K-theory of Z' after 2-adic completion.Comment: 36 pages ; see also http://www.math.jussieu.fr/~karoubi/ and
http://www.math.nus.edu.sg/~matberic
Homological realization of prescribed abelian groups via -theory
Using algebraic and topological K-theory together with complex C^*-algebras,
we prove that every abelian group may be realized as the centre of a strongly
torsion generated group whose integral homology is zero in dimension one and
isomorphic to two arbitrarily prescribed abelian groups in dimensions two and
three.Comment: 10 page
The homotopy fixed point theorem and the Quillen-Lichtenbaum conjecture in hermitian K-theory
Let X be a noetherian scheme of finite Krull dimension, having 2 invertible
in its ring of regular functions, an ample family of line bundles, and a global
bound on the virtual mod-2 cohomological dimensions of its residue fields. We
prove that the comparison map from the hermitian K-theory of X to the homotopy
fixed points of K-theory under the natural Z/2-action is a 2-adic equivalence
in general, and an integral equivalence when X has no formally real residue
field. We also show that the comparison map between the higher
Grothendieck-Witt (hermitian K-) theory of X and its \'etale version is an
isomorphism on homotopy groups in the same range as for the Quillen-Lichtenbaum
conjecture in K-theory. Applications compute higher Grothendieck-Witt groups of
complex algebraic varieties and rings of 2-integers in number fields, and hence
values of Dedekind zeta-functions.Comment: 17 pages, to appear in Adv. Mat
Homological realization of prescribed abelian groups via K-theory
Using algebraic and topological K-theory together with complex C*-algebras, we prove that every abelian group may be realized as the centre of a strongly torsion generated group whose integral homology is zero in dimension one and isomorphic to two arbitrarily prescribed abelian groups in dimensions two and thre
Phasing-out tobacco: proposal to deny access to tobacco for those born from 2000
As a contribution to worldwide efforts towards a tobacco-free society, this paper considers the possibility of a long-term phasing-in of a total ban, by proposing that individuals born in or after the year 2000 have their supply of tobacco restricted. In conjunction, a survey that we have conducted in Singapore indicates strong public support (even among current smokers) for the proposal
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