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Abstract: We review various aspects of the topological classification of D-branecharges in K-theory, focusing on techniques from geometric K-homology andKasparov-s KK-theory. The latter formulation enables an elaborate descriptionof D-brane charge on large classes of noncommutative spaces, and a refinedcharacterization of open string T-duality in terms of correspondences andKK-equivalence. The examples of D-branes on noncommutative Riemann surfaces andin constant H-flux backgrounds are treated in detail. Mathematicalconstructions include noncommutative generalizations of Poincare duality andK-orientation, characteristic classes, and the Riemann-Roch theorem.

Autor: Richard J. Szabo

Fuente: https://arxiv.org/

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