2005/07/21 by Carey, Alan L., Wang, Bai-Ling
#55N15 #55R50 #57R22 #81T13 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #K-Theory and Homology (math.KT)
paper · doi:10.48550/arxiv.math/0507414
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→ 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.