Thom isomorphism and Push-forward map in twisted K-theory

Details Thom isomorphism and Push-forward map in twisted K-theory Thom isomorphism and Push-forward map in twisted K-theory

2005-07-21

arxiv.org/abs/math/0507414v4

Mathematics

K-Theory and Homology

Add Remark 4.2 to clarify some confusions in the current literature about the role of automorphisms of twists and their action

Scientific paper

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 $f: X\to Y$ (not necessarily K-oriented). The push-forward map generalizes the push-forward map in ordinary K-theory for any $K$-oriented differentiable proper map and the Atiyah-Singer index theorem of Dirac operators on Clifford modules. For $D$-branes satisfying Freed-Witten's anomaly cancellation condition in a manifold with a non-trivial $B$-field, we associate a canonical element in the twisted K-group to get the so-called D-brane charges.

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