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Fiber products, Poincaré duality and $ A_\infty$-ring spectra


Author: John R. Klein
Journal: Proc. Amer. Math. Soc. 134 (2006), 1825-1833
MSC (2000): Primary 55N91, 57R19; Secondary 55P10, 55B20
DOI: https://doi.org/10.1090/S0002-9939-05-08148-7
Published electronically: October 25, 2005
MathSciNet review: 2207500
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Abstract: For a Poincaré duality space $ X^d$ and a map $ X \to B$, consider the homotopy fiber product $ X \times^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 \times^B X$ has the structure of a graded associative algebra. When $ X \to B$ is the diagonal map of a manifold $ X$, one recovers a result of Chas and Sullivan about the homology of the unbased loop space $ LX$.


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Additional Information

John R. Klein
Affiliation: Department of Mathematics, Wayne State University, Detroit, Michigan 48202
Email: klein@math.wayne.edu

DOI: https://doi.org/10.1090/S0002-9939-05-08148-7
Received by editor(s): October 17, 2004
Received by editor(s) in revised form: December 28, 2004
Published electronically: October 25, 2005
Additional Notes: The author was partially supported by NSF Grant DMS-0201695.
Communicated by: Paul Goerss
Article copyright: © Copyright 2005 by the author

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