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On the homology theory of fibre spaces
- Publication Year :
- 2005
-
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.<br />8 pages. This is the English version of the paper published originally in Russian
- Subjects :
- Discrete mathematics
Pure mathematics
General Mathematics
Cellular homology
Homology (mathematics)
Mathematics::Algebraic Topology
Cohomology
Tensor product
Mathematics::K-Theory and Homology
FOS: Mathematics
Algebraic Topology (math.AT)
Mathematics - Algebraic Topology
Algebraic number
Mathematics::Symplectic Geometry
55S30, 55R20, 55U15
Relative homology
Mathematics
Subjects
Details
- Language :
- Russian
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....9dc11b88cd3c2f420bca656a2fbd5d99