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Donald Stanley

2009-07-28
15:30:00 - 16:30:00

Rigid Poincare Duality

308 , Mathematics Research Center Building (ori. New Math. Bldg.)

The cohomology of a closed oriented manifold M forms a Poincare duality algebra. If M is formal, for example Kahler, then H^*(M) is quasi-isomorphic to C^*(M). So we can consider that we have Poincare duality on the chain level. We show that if we work over a field of characteristic 0 then C^*(M) is always quasi-isomorphic to a commutative differential graded algebra that satisfies Poincare duality. This allows the simplification of chain level formulas that involve Poincare duality. We give examples of such formulas coming from string topology and configuration spaces, and discuss comparisons between the Kahler and the general manifold cases.