2005/04/21 by Tornike Kadeishvili
Mathematics · #math.AT #msc:55S30 #msc:55R20 #msc:55U15
published as Uspekhi Mat. Nauk 35:3 (1980), 183-188 · 8 pages. This is the English version of the paper published originally in Russian
arxiv created 2005/04/21 · arxiv updated 2009/12/01
The A(\inft)-algebra structure in homology of a DG-algebra is constructed. This structure is unique up to isomorphism of A(∞) algebras. Connection of this structure with Massey products is indicated. The notion of A(∞)-module over an A(∞)-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(∞)-algebras. These algebraic results are used to describe homology of classifying spaces, cohomology of loop spaces, and homology of fibre bundles.