Feynman Diagrams and Low-Dimensional Topology

@inproceedings{Kontsevich1994FeynmanDA,
  title={Feynman Diagrams and Low-Dimensional Topology},
  author={M. Kontsevich},
  year={1994}
}
We shall describe a program here relating Feynman diagrams, topology of manifolds, homotopical algebra, non-commutative geometry and several kinds of “topological physics.” 
Weyl n-Algebras
We introduce Weyl n-algebras and show how their factorization complex may be used to define invariants of manifolds. In the appendix, we heuristically explain why these invariants must beExpand
Perturbative Topological Field Theory
We give a review of the application of perturbative techniques to topologi-cal quantum eld theories, in particular three-dimensional Chern-Simons-Witten theory and its various generalizations. ToExpand
Weyl n-algebras
We introduce Weyl n-algebras and show how their factorization homology may be used to define invariants of manifolds. In the appendix we heuristically explain why these invariants must beExpand
Combinatorics and algebra of tensor calculus
In this paper, motivated by the theory of operads and PROPs we reveal the combinatorial nature of tensor calculus for strict tensor categories and show that there exists a monad which is described byExpand
Homological algebra related to surfaces with boundary
In this article we describe an algebraic framework which can be used in three related but different contexts: string topology, symplectic field theory, and Lagrangian Floer theory of higher genus. ItExpand
Topological Field Theories and Harrison Homology
Tools and arguments developed by Kevin Costello are adapted to families of “Outer Spaces” or spaces of graphs. This allows us to prove a version of Deligne’s conjecture: the Harrison homologyExpand
Homotopy Gerstenhaber algebras and topological field theory
We prove that the BRST complex of a topological conformal field theory is a homotopy Gerstenhaber algebra, as conjectured by Lian and Zuckerman in 1992. We also suggest a refinement of the originalExpand
Graph cohomology classes in the Batalin-Vilkovisky formalism
This paper gives a conceptual formulation of Kontsevich’s ‘dual construction’ producing graph cohomology classes from a differential graded Frobenius algebra with an odd scalar product. OurExpand
On operad structures of moduli spaces and string theory
We construct a real compactification of the moduli space of punctured rational algebraic curves and show how its geometry yields operads governing homotopy Lie algebras, gravity algebras andExpand
Abstract Hodge Decomposition and Minimal Models for Cyclic Algebras
We show that an algebra over a cyclic operad supplied with an additional linear algebra datum called Hodge decomposition admits a minimal model whose structure maps are given in terms of summationExpand
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