252 research outputs found
On positivity of the Kadison constant and noncommutative Bloch theory
In an earlier paper, we established a natural connection between the
Baum-Connes conjecture and noncommutative Bloch theory, viz. the spectral
theory of projectively periodic elliptic operators on covering spaces. We
elaborate on this connection here and provide significant evidence for a
fundamental conjecture in noncommutative Bloch theory on the non-existence of
Cantor set type spectrum. This is accomplished by establishing an explicit
lower bound for the Kadison constant of twisted group C*-algebras in a large
number of cases, whenever the multiplier is rational.Comment: Latex2e, 16 pages, final version, to appear in a special issue of
Tohoku Math. J. (in press
Witten Genus and Elliptic genera for proper actions
In this paper, we construct for the first time, the Witten genus and elliptic
genera on noncompact manifolds with a proper cocompact action by an almost
connected Lie group and prove vanishing and rigidity results that generalise
known results for compact group actions on compact manifolds. We also compute
our genera for some interesting examples.Comment: 26 pages. A conjecture remove
T-duality of current algebras and their quantization
In this paper we show that the T-duality transform of Bouwknegt, Evslin and
Mathai applies to determine isomorphisms of certain current algebras and their
associated vertex algebras on topologically distinct T-dual spacetimes
compactified to circle bundles with -flux.Comment: 21 pages. 3 references added and to appear in Contemp. Mat
On the homotopy invariance of L^2 torsion for covering spaces
We prove the homotopy invariance of L^2 torsion for covering spaces, whenever
the covering transformation group is either residually finite or amenable. In
the case when the covering transformation group is residually finite and when
the L^2 cohomology of the covering space vanishes, the homotopy invariance was
established earlier by Lueck. We also give some applications of our results.Comment: LaTeX2e, 10 page
Holomorphic Quillen determinant line bundles on integral compact Kahler manifolds
We show that any compact Kahler manifold with integral Kahler form,
parametrizes a natural holomorphic family of Cauchy-Riemann operators on the
Riemann sphere such that the Quillen determinant line bundle of this family is
isomorphic to a sufficiently high tensor power of the holomorphic line bundle
determined by the integral Kahler form. We also establish a symplectic version
of the result. We conjecture that an equivariant version of our result is true.Comment: Latex2e, 10 pages, To appear in, Quillen memorial issue, Quarterly J.
Mat
Higher abelian gauge theory associated to gerbes on noncommutative deformed M5-branes and S-duality
We enhance the action of higher abelian gauge theory associated to a gerbe on
an M5-brane with an action of a torus , by a
noncommutative -deformation of the M5-brane. The ingredients of
the noncommutative action and equations of motion include the deformed Hodge
duality, deformed wedge product, and the noncommutative integral over the
noncommutative space obtained by strict deformation quantization. As an
application we then introduce a variant model with an enhanced action in which
we show that the corresponding partition function is a modular form, which is a
purely noncommutative geometry phenomenon since the usual theory only has a
-symmetry. In particular, S-duality in this 6-dimensional higher
abelian gauge theory model is shown to be, in this sense, on par with the usual
4-dimensional case.Comment: 23 pages, details and references adde
On mysteriously missing T-duals, H-flux and the T-duality group
A general formula for the topology and H-flux of the T-duals of type II
string theories with H-flux on toroidal compactifications is presented here. It
is known that toroidal compactifications with H-flux do not necessarily have
T-duals which are themselves toroidal compactifications. A big puzzle has been
to explain these mysterious ``missing T-duals'', and our paper presents a
solution to this problem using noncommutative topology. We also analyze the
T-duality group and its action, and illustrate these concepts with examples.Comment: 4 pages, latex2e, Mistake in formula corrected, ref. adde
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