On the homology theory of fibre spaces

Abstract

The $A(\inft)$-algebra structure in homology of a DG-algebra is constructed. This structure is unique up to isomorphism of $A(\infty )$ algebras. Connection of this structure with Massey products is indicated. The notion of $A(\infty )$-module over an $A(\infty )$-algebra is introduced and such a structure is constructed in homology of a DG-modules over a DG-algebra. The theory of twisted tensor products is generalized from the case of DG-algebras to the case of $A(\infty )$-algebras. These algebraic results are used to describe homology of classifying spaces, cohomology of loop spaces, and homology of fibre bundles.

8 pages. This is the English version of the paper published originally in Russian