  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.
