Feynman diagrams and minimal models for operadic algebras

@article{Chuang2008FeynmanDA,
  title={Feynman diagrams and minimal models for operadic algebras},
  author={Joseph Chuang and Andrey Lazarev},
  journal={Journal of the London Mathematical Society},
  year={2008},
  volume={81}
}
  • J. Chuang, A. Lazarev
  • Published 24 February 2008
  • Mathematics
  • Journal of the London Mathematical Society
We construct an explicit minimal model for an algebra over the cobar‐construction of a differential graded operad. The structure maps of this minimal model are expressed in terms of sums over decorated trees. We introduce the appropriate notion of a homotopy equivalence of operadic algebras and show that our minimal model is homotopy equivalent to the original algebra. All this generalizes and gives a conceptual explanation of well‐known results for A∞‐algebras. Furthermore, we show that these… 
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References

SHOWING 1-10 OF 50 REFERENCES
Dual Feynman transform for modular operads
We introduce and study the notion of a dual Feynman transform of a modular operad. This generalizes and gives a conceptual explanation of Kontsevich's dual construction producing graph cohomology
Modular Operads
We develop a \higher genus" analogue of operads, which we call modular operads, in which graphs replace trees in the deenition. We study a functor F on the category of modular operads, the Feynman
Cohomology theories for homotopy algebras and noncommutative geometry
This paper builds a general framework in which to study cohomology theories of strongly homotopy algebras, namely A∞–, C∞– and L∞–algebras. This framework is based on noncommutative geometry as
ASSOCIAHEDRA, CELLULAR W -CONSTRUCTION AND PRODUCTS OF A∞-ALGEBRAS
The aim of this paper is to construct a functorial tensor product of A∞-algebras or, equivalently, an explicit diagonal for the operad of cellular chains, over the integers, of the Stasheff
Strongly homotopy algebras of a K\"ahler manifold
It is shown that any compact K\"ahler manifold $M$ gives canonically rise to two strongly homotopy algebras, the first one being associated with the Hodge theory of the de Rham complex and the second
Symplectic C∞-algebras
In this paper we show that a strongly homotopy commutative (or C∞-) algebra with an invariant inner product on its cohomology can be uniquely extended to a symplectic C∞-algebra (an ∞-generalisation
Associahedra, cellular W-construction and products of $A_\infty$-algebras
The aim of this paper is to construct a functorial tensor product of A ∞ -algebras or, equivalently, an explicit diagonal for the operad of cellular chains, over the integers, of the Stasheff
Loop Homotopy Algebras in Closed String Field Theory
Abstract: Barton Zwiebach constructed [20] “string products” on the Hilbert space of a combined conformal field theory of matter and ghosts, satisfying the “main identity”. It has been well known
...
1
2
3
4
5
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