On the homology theory of fibre spaces

Details On the homology theory of fibre spaces On the homology theory of fibre spaces

2005-04-21

arxiv.org/abs/math/0504437v1

Uspekhi Mat. Nauk 35:3 (1980), 183-188

Mathematics

Algebraic Topology

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

Scientific paper

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.

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