D-branes and bivariant K-theory
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Publication:5418228
zbMATH Open1293.81036arXiv0809.3029MaRDI QIDQ5418228
Publication date: 3 June 2014
Abstract: 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.
Full work available at URL: https://arxiv.org/abs/0809.3029
String and superstring theories; other extended objects (e.g., branes) in quantum field theory (81T30) Research exposition (monographs, survey articles) pertaining to quantum theory (81-02) Noncommutative geometry methods in quantum field theory (81T75) (K)-theory and homology; cyclic homology and cohomology (19D55) Noncommutative global analysis, noncommutative residues (58J42)
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