On the cohomology of the free loop space of a 4- dimensional manifold

Abstract

In this paper we consider a theorem of Feigin and Tsygan that is about the gereralized free product of a pushout diagram (Theorem 2 below) and try to show that it can be generalized, i e., the theorem is satisfied in the more general case than that they have stated. In order to do this, we formulate a conjecture stating the validity of such generalizatzon. To support the conjecture we use it in two different computations, and show that the results of these computations coincide with the results that C. Löfwall has proved in a different way.

I wish to thank J. E. Roos who called my attention to this problem. I am grateful to him because of his great help and good advice during the work on this paper. I wish to thank Ralf Fröberg, L Lambe, and C Löfwall for stimulating discussions.