Fiber products, Poincare duality and A_\infty-ring spectra
Algebraic Topology
2007-05-23 v1 Geometric Topology
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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Cite
@article{arxiv.math/0306350,
title = {Fiber products, Poincare duality and A_\infty-ring spectra},
author = {John R. Klein},
journal= {arXiv preprint arXiv:math/0306350},
year = {2007}
}
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12 pages