# Simplicial and Operad Methods in Algebraic Topology

@inproceedings{Smirnov2001SimplicialAO, title={Simplicial and Operad Methods in Algebraic Topology}, author={Valerii A. Smirnov}, year={2001} }

Operads in the category of topological spaces Simplicial objects and homotopy theory Algebraic structures on chain complexes $A_\infty$-structures on chain complexes Operads and algebras over operads Homoloty of iterated loop spaces Homotopy theories and $E_\infty$-structures Operad methods in cobordism theory Description of the cohomology of groups and algebras Homology operations and differentials in the Adams spectral sequence Bibliography Index.

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## The tensor functor from the category of $A_\infty$-algebras into the category of differential modules with $\infty$-simplicial faces.

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## Homotopy properties of differential modules with simplicial F∞-faces and D∞-differential modules

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## Holonomy, twisting cochains and characteristic classes

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## Holonomy, twisting cochains and characteristic classes

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## The homotopy invariance of cyclic homology of $A_\infty$-algebras over rings.

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## The homotopy invariance of cyclic homology of A ∞-algebras over rings

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## The homotopy invariance of dihedral homology of involutive $A_\infty$-algebras over rings

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#### References

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## He introduced the concept of an operad E as a family of topological spaces E(j), j ≥ 0, whose points should be thought of as abstract j-ary operations

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