|XXV Workshop on Geometric Methods in Physics||2-8.07.2006|
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Poincare duality on noncommutative manifolds
Poincare duality is a central property of differentiable manifolds. Reasearch in noncommutative geometry suggests possible ways of extending this notion to noncommutative analogues of manifolds. This talk will provide an overview of the main mathematical tools that are required in this transition, including KK-theory and cyclic type homology theories. We shall provide examples of how this formalism can be used in the theory of D-branes.