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A Path Integral Approach¶to the Kontsevich Quantization Formula

- A. Cattaneo, G. Felder
- Mathematics, Physics
- 15 February 1999

Abstract: We give a quantum field theory interpretation of Kontsevich's deformation quantization formula for Poisson manifolds. We show that it is given by the perturbative expansion of the path… Expand

Poisson sigma models and symplectic groupoids

- A. Cattaneo, G. Felder
- Mathematics
- 3 March 2000

We consider the Poisson sigma model associated to a Poisson manifold. The perturbative quantization of this model yields the Kontsevich star product formula. We study here the classical model in the… Expand

Relative formality theorem and quantisation of coisotropic submanifolds

- A. Cattaneo, G. Felder
- Mathematics
- 29 January 2005

On the AKSZ Formulation of the Poisson Sigma Model

- A. Cattaneo, G. Felder
- Mathematics
- 14 February 2001

We review and extend the Alexandrov–Kontsevich–Schwarz–Zaboronsky construction of solutions of the Batalin–Vilkovisky classical master equation. In particular, we study the case of sigma models on… Expand

Integral invariants of 3-manifolds. II

- R. Bott, A. Cattaneo
- Mathematics
- 13 February 1998

This note is a sequel to our earlier paper of the same title [4] and describes invariants of rational homology 3-spheres associated to acyclic orthogonal local systems. Our work is in the spirit of… Expand

Coisotropic submanifolds in Poisson geometry and branes in the Poisson sigma model

- A. Cattaneo, G. Felder
- Mathematics
- 10 September 2003

Abstract.General boundary conditions (‘branes’) for the Poisson sigma model are studied. They turn out to be labeled by coisotropic submanifolds of the given Poisson manifold. The role played by… Expand

Configuration spaces and Vassiliev classes in any dimension

- A. Cattaneo, P. Cotta-Ramusino, Riccardo Longoni
- Mathematics
- 26 October 1999

The real cohomology of the space of imbeddings of S 1 into R n , n> 3, is studied by using conguration space integrals. Nontrivial classes are explicitly constructed. As a by-product, we prove the… Expand

Introduction to supergeometry

- A. Cattaneo, F. Schaetz
- Mathematics
- 15 November 2010

These notes are based on a series of lectures given by the first author at the school of "Poisson 2010", held at IMPA, Rio de Janeiro. They contain an exposition of the theory of super- and graded… Expand

From local to global deformation quantization of Poisson manifolds

- A. Cattaneo, G. Felder, L. Tomassini
- Mathematics
- 22 December 2000

We give an explicit construction of a deformation quantization of the algebra of functions on a Poisson manifold, based on M. Kontsevich's local formula. The deformed algebra of functions is realized… Expand

On the Globalization of Kontsevich's Star Product and the Perturbative Poisson Sigma Model

- A. Cattaneo, G. Felder
- Mathematics
- 4 November 2001

The globalization of Kontsevich's local formula (resp., the perturbative expansion of the Poisson sigma model) is described in down-to-earth terms.

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