Related papers: Crystallographic T-duality

T-duality of gauge theories on a noncommutative $T^d$ can be extended to include fields with twisted boundary conditions. The resulting T-dual theories contain novel nonlocal fields. These fields represent dipoles of constant magnitude.…

We introduce the notion of K-theoretic duality for extensions of separable unital nuclear $C^*$-algebras by using K-homology long exact sequence and cyclic six term exact sequence for K-theory groups of extensions. We then prove that the…

We extend the notion of topological T-duality from oriented sphere bundles to transgressive fibrations, a more general type fibration characterised by the abundance of transgressive elements. Examples of transgressive fibrations include…

In this article we give a characterisation of the Baum-Connes assembly map with coefficients. The technical tools needed are the K-theory of C*-categories, and equivariant KK-theory in the world of groupoids.

Representing the data of a string compactified on a circle in the background of H-flux in terms of the geometric data of a principal loop group bundle, we show that T-duality in type II string theory can be understood as the interchange of…

The full U-duality symmetry of toroidally compactified M-theory can only be displayed by allowing non-rectangular tori with expectation values of the gauge fields. We construct an E_d(Z) U-duality invariant mass formula incorporating…

This is a study of twisted K-theory on a product space $T \times M$. The twisting comes from a decomposable cup product class which applies the 1-cohomology of $T$ and the 2-cohomology of $M$. In the case of a topological product, we give a…

We show that the supermembrane theory compactified on a torus is invariant under T-duality. There are two different topological sectors of the compactified supermembrane (M2) classified according to a vanishing or nonvanishing second…

We compute the equivariant $K$-homology of the classifying space for proper actions, for compact 3-dimensional hyperbolic reflection groups. This coincides with the topological $K$-theory of the reduced $C^\ast$-algebra associated to the…

Twisted K-theory has its origins in the author's PhD thesis [27] : http://www.numdam.org/item?id=ASENS_1968_4_1_2_161_0 and in the paper with P. Donovan http://www.numdam.org/item?id=PMIHES_1970__38__5_0 The objective of this paper is to…

String compactifications with T-duality twists are revisited and the gauge algebra of the dimensionally reduced theories calculated. These reductions can be viewed as string theory on T-fold backgrounds, and can be formulated in a `doubled…

We present an abstract unifying framework for interpreting Stone-type dualities; several known dualities are seen to be instances of just one topos-theoretic phenomenon, and new dualities are introduced. In fact, infinitely many new…

The Lichtenbaum-Quillen conjecture for smooth complex varieties states that algebraic and topological K-theory with finite coefficients become isomorphic in high degrees. We define the "Lichtenbaum-Quillen dimension" of a variety in terms…

Although the introduction of generalised and extended geometry has been motivated mainly by the appearance of dualities upon reductions on tori, it has until now been unclear how (all) the duality transformations arise from first principles…

Let the discrete group G act properly and isometrically on the Riemannian manifold X. Let C_0(X, \delta) be the section algebra of a smooth locally trivial G-equivariant bundle of elementary C*-algebras representing an element \delta of the…

Equivariant T-duality triples of locally compact abelian groups are considered. The motivating example dealing with the group $\R^n$ containing a lattice $\Z^n$ comes with an isomorphism in twisted equivariant K-theory.

We introduce a theory of multigraded Cayley-Chow forms associated to subvarieties of products of projective spaces. Two new phenomena arise: first, the construction turns out to require certain inequalities on the dimensions of projections;…

In one of our previous papers we generalized the Buscher T-dualization procedure. Here we will investigate the application of this procedure to the theory of a bosonic string moving in the weakly curved background. We obtain the complete…

The K-theoretic analog of Spanier-Whitehead duality for noncommutative C*-algebras is shown to hold for the Ruelle algebras associated to irreducible Smale spaces. This had previously been proved only for shifts of finite type. Implications…

We study the topology of T-duality for pairs of U(1)-bundles and three-dimensional integral cohomology classes over orbispaces. In particular, our results apply to U(1)-spaces with finite isotropy. We generalize the theory developed in our…