D-branes and bivariant K-theory

Details D-branes and bivariant K-theory D-branes and bivariant K-theory

2008-09-17

arxiv.org/abs/0809.3029v1

Physics

High Energy Physics

High Energy Physics - Theory

45 pages; Based on invited lectures given at the workshop "Noncommutative Geometry and Physics 2008 - K-Theory and D-Brane -",

Scientific paper

We review various aspects of the topological classification of D-brane charges in K-theory, focusing on techniques from geometric K-homology and Kasparov's KK-theory. The latter formulation enables an elaborate description of D-brane charge on large classes of noncommutative spaces, and a refined characterization of open string T-duality in terms of correspondences and KK-equivalence. The examples of D-branes on noncommutative Riemann surfaces and in constant H-flux backgrounds are treated in detail. Mathematical constructions include noncommutative generalizations of Poincare duality and K-orientation, characteristic classes, and the Riemann-Roch theorem.

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