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.

arXiv comment8 pages. This is the English version of the paper published originally in Russian

Cited by in corpus (5)

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• A relative version of the ordinary perturbation lemma
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• Towards Homological Mirror Symmetry
• A partial $A_{\infty }$-structure on the cohomology of $C_n\times C_m$