Thom isomorphism and Push-forward map in twisted K-theory
K-Theory and Homology
2007-05-23 v4 High Energy Physics - Theory
Differential Geometry
Abstract
We establish the Thom isomorphism in twisted K-theory for any real vector bundle and develop the push-forward map in twisted K-theory for any differentiable proper map (not necessarily K-oriented). The push-forward map generalizes the push-forward map in ordinary K-theory for any -oriented differentiable proper map and the Atiyah-Singer index theorem of Dirac operators on Clifford modules. For -branes satisfying Freed-Witten's anomaly cancellation condition in a manifold with a non-trivial -field, we associate a canonical element in the twisted K-group to get the so-called D-brane charges.
Cite
@article{arxiv.math/0507414,
title = {Thom isomorphism and Push-forward map in twisted K-theory},
author = {Alan L. Carey and Bai-Ling Wang},
journal= {arXiv preprint arXiv:math/0507414},
year = {2007}
}
Comments
Add Remark 4.2 to clarify some confusions in the current literature about the role of automorphisms of twists and their action on twisted K-theroy