Related papers: Thom isomorphism and Push-forward map in twisted K…

In the present paper we describe the action of (not necessarily line) bundles of finite order on the $K$-functor in terms of classifying spaces. This description might provide with an approach for more general twistings in $K$-theory than…

There are fundamental open problems in the precise global nature of RR-field tadpole cancellation conditions in string theory. Moreover, the non-perturbative lift as M5/MO5-anomaly cancellation in M-theory had been based on indirect…

We introduce a general theory of parametrized objects in the setting of infinity categories. Although spaces and spectra parametrized over spaces are the most familiar examples, we establish our theory in the generality of objects of a…

For a Lie groupoid G with a twisting (a PU(H)-principal bundle over G), we use the (geometric) deformation quantization techniques supplied by Connes tangent groupoids to define an analytic index morphism in twisted K-theory. In the case…

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…

Perturbations due to round-off errors in computer modeling are discontinuous and therefore one cannot use results like KAM theory about smooth perturbations of twist maps. We elaborate a special approximation scheme to construct two smooth…

We discuss the relation between the Ramond-Ramond charges of D-branes and the topology of Chan-Paton vector bundles. We show that a topologically nontrivial normal bundle induces RR charge and that the result fits in perfectly with the…

Twisted K-theory on a manifold X, with twisting in the 3rd integral cohomology, is dis- cussed in the case when X is a product of a circle T and a manifold M. The twist is assumed to be decomposable as a cup product of the basic integral…

Let G be a compact, simply connected Lie group. We develop a `quantization functor' from pre-quantized quasi-Hamiltonian G-spaces at level k to the fusion ring (Verlinde algebra) R_k(G). The quantization Q(M) is defined as a push-forward in…

We investigate the K-theory of twisted higher-rank-graph algebras by adapting parts of Elliott's computation of the K-theory of the rotation algebras. We show that each 2-cocycle on a higher-rank graph taking values in an abelian group…

We give a proof of the cobordism invariance of the index of elliptic pseudodifferential operators on sigma-compact manifolds, where, in the non-compact case, the operators are assumed to be multiplication outside a compact set. We show…

We study global worldsheet anomalies for open strings ending on several coincident D-branes in the presence of a B-field. We show that cancellation of anomalies is made possible by a correlation between the t'Hooft magnetic flux on the…

We study RR charge cancellation consistency conditions in string compactifications with open string sectors, by introducing D-brane probes in the configuration. We show that uncancelled charges manifest as chiral gauge anomalies in the…

Extending ideas of twisted equivariant $K$-theory, we construct twisted versions of the representation rings for Lie superalgebras and Lie supergroups, built from projective $\Z_{2}$-graded representations with a given cocycle. We then…

Using a combination of Atiyah-Segal ideas on one side and of Connes and Baum-Connes ideas on the other, we prove that the Twisted geometric K-homology groups of a Lie groupoid have an external multiplicative structure extending hence the…

The charges of the twisted D-branes of certain WZW models are determined. The twisted D-branes are labelled by twisted representations of the affine algebra, and their charge is simply the ground state multiplicity of the twisted…

We establish Thom's jet transversality theorem for regular maps from an affine algebraic manifold to an algebraic manifold satisfying a suitable flexibility condition. It can be considered as the algebraic version of Forstneri\v{c}'s jet…

By a small bundle gerbe we mean a bundle gerbe in the sense of Murray defined on a smooth, finite-dimensional, fibre bundle over a manifold. We construct such gerbes over compact oriented aspherical 3-manifolds, as well as in higher…

We show that the Atiyah-Hirzebruch K-theory of spaces admits a canonical generalization for stratified spaces. For this we study algebraic constructions on stratified vector bundles. In particular the tangent bundle of a stratified manifold…

This is an expository account of the following result: we can construct a group by means of twisted Z_2-graded vectorial bundles which is isomorphic to K-theory twisted by any degree three integral cohomology class.