# Differential Twisted K-theory and Applications

@article{Carey2007DifferentialTK, title={Differential Twisted K-theory and Applications}, author={Alan L. Carey and Jouko Mickelsson and Bai-Ling Wang}, journal={arXiv: K-Theory and Homology}, year={2007} }

In this paper, we develop differential twisted K-theory and define a twisted Chern character on twisted K-theory which depends on a choice of connection and curving on the twisting gerbe. We also establish the general Riemann-Roch theorem in twisted K-theory and find some applications in the study of twisted K-theory of compact simple Lie groups.

#### 28 Citations

Chern-Weil Construction for Twisted K-Theory

- Mathematics
- 2010

We give a finite-dimensional and geometric construction of a Chern character for twisted K-theory, introducing a notion of connection on a twisted vectorial bundle which can be considered as a… Expand

Riemann-Roch and index formulae in twisted K-theory

- Physics, Mathematics
- 2009

In this paper, we establish the Riemann-Roch theorem in twisted K-theory extending our earlier results. As an application, we prove a twisted index formula and show that D-brane charges in Type I and… Expand

Geometric models of twisted differential K-theory I

- Mathematics
- 2016

This is the first in a series of papers constructing geometric models of twisted differential K-theory. In this paper we construct a model of even twisted differential K-theory when the underlying… Expand

T-DUALITY AND DIFFERENTIAL K-THEORY

- Mathematics, Physics
- 2014

We give a precise formulation of T-duality for Ramond–Ramond fields. This gives a canonical isomorphism between the "geometrically invariant" subgroups of the twisted differentialK-theory groups… Expand

Twisted differential cohomology

- Mathematics
- 2014

The main goal of the present paper is the construction of twisted generalized differential cohomology theories and the comprehensive statement of its basic functorial properties. Technically it… Expand

TWISTED BUNDLES AND TWISTED K-THEORY

- Mathematics
- 2010

We offer here a more direct approach to twisted K-theory, based on the notion of twisted vector bundles (of finite or infinite dimension) and of twisted principal bundles. This is closeely related to… Expand

Topological T-duality for general circle bundles

- Mathematics
- 2011

We extend topological T-duality to the case of general circle bundles. In this setting we prove existence and uniqueness of T-duals. We then show that T-dual spaces have isomorphic twisted… Expand

Differential K-theory. A survey

- Mathematics, Physics
- 2010

Generalized differential cohomology theories, in particular differential K-theory (often called “smooth K-theory”), are becoming an important tool in differential geometry and in mathematical… Expand

Differential K-Theory: A Survey

- Mathematics
- 2012

Generalized differential cohomology theories, in particular differential K-theory (often called “smooth K-theory”), are becoming an important tool in differential geometry and in mathematical… Expand

Mickelsson's twisted K-theory invariant and its generalizations

- Mathematics
- 2013

Mickelsson's invariant is an invariant of certain odd twisted K-classes of compact oriented three dimensional manifolds. We reformulate the invariant as a natural homomorphism taking values in a… Expand

#### References

SHOWING 1-10 OF 106 REFERENCES

Twisted K-theory and cohomology

- Mathematics
- 2005

We explore the relations of twisted K-theory to twisted and untwisted classical cohomology. We construct an Atiyah-Hirzebruch spectral sequence, and describe its differentials rationally as Massey… Expand

Twisted K-Theory and K-Theory of Bundle Gerbes

- Mathematics, Physics
- 2002

Abstract: In this note we introduce the notion of bundle gerbe K-theory and investigate the relation to twisted K-theory. We provide some examples. Possible applications of bundle gerbe K-theory to… Expand

Twisted K-theory and loop groups

- Mathematics, Materials Science
- 2002

Twisted /("-theory has received much attention recently in both math ematics and physics. We describe some models of twisted /("-theory, both topological and geometric. Then we state a theorem which… Expand

Twisted K-theory and loop group representations

- Mathematics, Physics
- 2003

This is the third paper of a series relating the equivariant twisted $K$-theory of a compact Lie group $G$ to the ``Verlinde space'' of isomorphism classes of projective lowest-weight representations… Expand

On the twisted K-homology of simple Lie groups

- Mathematics
- 2004

We prove that the twisted K-homology of a simply connected simple Lie group G of rank n is an exterior algebra on n-1 generators tensor a cyclic group. We give a detailed description of the order of… Expand

An approach toward a finite-dimensional definition of twisted K-theory

- Mathematics
- 2006

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… Expand

Twisted K-theory of Lie groups

- Physics, Mathematics
- 2004

I determine the twisted K-theory of all compact simply connected simple Lie groups. The computation reduces via the Freed-Hopkins-Teleman theorem [1] to the CFT prescription, and thus explains why it… Expand

Families Index Theorem in Supersymmetric WZW Model and Twisted K-Theory: The SU(2) Case

- Mathematics, Physics
- 2005

The construction of twisted K-theory classes on a compact Lie group is reviewed using the supersymmetric Wess-Zumino-Witten model on a cylinder. The Quillen superconnection is introduced for a family… Expand

Chern Character in Twisted K-Theory: Equivariant and Holomorphic Cases

- Physics, Mathematics
- 2003

Abstract: It was argued in [25, 5] that in the presence of a nontrivial B-field, D-brane charges in type IIB string theories are classified by twisted K-theory. In [4], it was proved that twisted… Expand

Twisted K-theory

- Mathematics
- 2004

Twisted complex K-theory can be defined for a space X equipped with a bundle of complex projective spaces, or, equivalently, with a bundle of C ∗ -algebras. Up to equivalence, the twisting… Expand