# 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.”

#### 465 Citations

Weyl n-Algebras

- Mathematics
- 2017

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 be… Expand

Perturbative Topological Field Theory

- Physics
- 1994

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. To… Expand

Weyl n-algebras

- Mathematics
- 2015

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 be… Expand

Combinatorics and algebra of tensor calculus

- Mathematics
- 2015

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 by… Expand

Homological algebra related to surfaces with boundary

- Mathematics
- 2015

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. It… Expand

Topological Field Theories and Harrison Homology

- Mathematics
- 2013

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 homology… Expand

Homotopy Gerstenhaber algebras and topological field theory

- Mathematics, Physics
- 1996

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 original… Expand

Graph cohomology classes in the Batalin-Vilkovisky formalism

- Mathematics, Physics
- 2009

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. Our… Expand

On operad structures of moduli spaces and string theory

- Physics, Mathematics
- 1995

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 and… Expand

Abstract Hodge Decomposition and Minimal Models for Cyclic Algebras

- Mathematics
- 2009

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 summation… Expand

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It is shown that 2+1 dimensional quantum Yang-Mills theory, with an action consisting purely of the Chern-Simons term, is exactly soluble and gives a natural framework for understanding the Jones… Expand

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