Fiber products, Poincaré duality and -ring spectra

Author:
John R. Klein

Journal:
Proc. Amer. Math. Soc. **134** (2006), 1825-1833

MSC (2000):
Primary 55N91, 57R19; Secondary 55P10, 55B20

Published electronically:
October 25, 2005

MathSciNet review:
2207500

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Abstract | References | Similar Articles | Additional Information

Abstract: For a Poincaré duality space and a map , consider the homotopy fiber product . If is orientable with respect to a multiplicative cohomology theory , then, after suitably regrading, it is shown that the -homology of has the structure of a graded associative algebra. When is the diagonal map of a manifold , one recovers a result of Chas and Sullivan about the homology of the unbased loop space .

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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:
http://dx.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