# 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.

#### Citations

##### Publications citing this paper.
SHOWING 1-10 OF 31 CITATIONS

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

VIEW 6 EXCERPTS
CITES BACKGROUND
HIGHLY INFLUENCED

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

VIEW 6 EXCERPTS
CITES BACKGROUND & METHODS
HIGHLY INFLUENCED

## Holonomy, twisting cochains and characteristic classes

VIEW 9 EXCERPTS
CITES BACKGROUND & METHODS
HIGHLY INFLUENCED

## Holonomy, twisting cochains and characteristic classes

VIEW 6 EXCERPTS
CITES BACKGROUND
HIGHLY INFLUENCED

VIEW 1 EXCERPT
CITES BACKGROUND

VIEW 1 EXCERPT
CITES BACKGROUND

VIEW 1 EXCERPT
CITES BACKGROUND

• Mathematics
• 2017

## A Foundation for Props, Algebras, and Modules

• Mathematics
• 2015

#### References

##### Publications referenced by this paper.
SHOWING 1-2 OF 2 REFERENCES

## 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

• A general method for describing many-placed operatio in
• An action of an operad E on a topological space X is a family of operations E(j)× X×j → X . By restricting these operations to points of
• 1972
VIEW 1 EXCERPT

## Stasheff in 1963 with the goal of describing loop spaces. He proved that a connected CW-complex

• J D.
• A∞-structure,
• 1963