Poincare Duality and Spin^c Structures for Noncommutative Manifolds

Details Poincare Duality and Spin^c Structures for Noncommutative Manifolds Poincare Duality and Spin^c Structures for Noncommutative Manifolds

2001-07-13

arxiv.org/abs/math-ph/0107013v1

Physics

Mathematical Physics

11 pages

Scientific paper

We prove a noncompact Serre-Swan theorem characterising modules which are sections of vector bundles not necessarily trivial at infinity. We then identify the endomorphism algebras of the resulting modules. The endomorphism results continue to hold for the generalisation of these modules to noncommutative, nonunital algebras. Finally, we apply these results to not necessarily compact noncommutative spin manifolds, proving that Poincare Duality implies the Morita equivalence of the `algebra of functions' and the `Clifford algebra.'

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