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Fiber products, Poincare duality and A_\infty-ring spectra

John R. Klein
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Abstract

For a Poincare duality space X and a map X -> B, consider the homotopy fiber product X x^B X. If X is orientable with respect to a multiplicative cohomology theory E, then, after suitably regrading, it is shown that the E-homology of X x^B X has the structure of a graded associative algebra. When X -> B is the diagonal map of a manifold X, one recovers a result of Chas and Sullivan about the homology of the free loop space LX.

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John R. Klein. 2003-06-24. Fiber products, Poincare duality and A_\infty-ring spectra. https://arxiv.org/abs/math/0306350

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