417 citations · 2.4k across the 99 of their papers we have counts for
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Biquantization of symmetric pairs and the quantum shift
Alberto S. Cattaneo, Carlo A. Rossi, Charles Torossian
The biquantization of symmetric pairs was studied in Cattaneo and Torossian in terms of Kontsevich-like graphs. This paper, also in view of recent results in Calaque et al, amends…
The character map in deformation quantization
Alberto S. Cattaneo, Giovanni Felder, Thomas Willwacher
The third author recently proved that the Shoikhet-Dolgushev L-infinity-morphism from Hochschild chains of the algebra of smooth functions on manifold to differential forms extends…
Remarks on Chern-Simons invariants
Alberto S. Cattaneo, Pavel Mnev
The perturbative Chern-Simons theory is studied in a finite-dimensional version or assuming that the propagator satisfies certain properties (as is the case, e.g., with the propaga…
Equivalences of Higher Derived Brackets
Alberto S. Cattaneo, Florian Schaetz
This note elaborates on Th. Voronov's construction [math/0304038,math/0412202] of -structures via higher derived brackets with a Maurer-Cartan element. It is shown that g…
Deformation Quantization and Reduction
Alberto S. Cattaneo
This note is an overview of the Poisson sigma model (PSM) and its applications in deformation quantization. Reduction of coisotropic and pre-Poisson submanifolds, their appearance…
On the Hochschild-Kostant-Rosenberg map for graded manifolds
Alberto S. Cattaneo, Domenico Fiorenza, Riccardo Longoni
We show that the Hochschild-Kostant-Rosenberg map from the space of multivector fields on a graded manifold N (endowed with a Berezinian volume) to the cohomology of the algebra of…
Relative formality theorem and quantisation of coisotropic submanifolds
Alberto S. Cattaneo, Giovanni Felder
We prove a relative version of Kontsevich's formality theorem. This theorem involves a manifold M and a submanifold C and reduces to Kontsevich's theorem if C=M. It states that the…
Formality and Star Products
Alberto S. Cattaneo, Davide Indelicato
These notes, based on the mini-course given at the PQR2003 Euroschool held in Brussels in 2003, aim to review Kontsevich's formality theorem together with his formula for the star…
Coisotropic submanifolds in Poisson geometry and branes in the Poisson sigma model
Alberto S. Cattaneo, Giovanni Felder
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 play…
Fedosov connections on jet bundles and deformation quantization
Alberto S. Cattaneo, Giovanni Felder, Lorenzo Tomassini
We review our construction of star-products on Poisson manifolds and discuss some examples. In particular, we work out the relation with Fedosov's original construction in the symp…
On the AKSZ formulation of the Poisson sigma model
Alberto S. Cattaneo, Giovanni Felder
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…
From local to global deformation quantization of Poisson manifolds
Alberto S. Cattaneo, Giovanni Felder, Lorenzo Tomassini
We give an explicit construction of a deformation quantization of the algebra of functions on a Poisson manifolds, based on Kontsevich's local formula. The deformed algebra of func…
Higher-dimensional BF theories in the Batalin-Vilkovisky formalism: The BV action and generalized Wilson loops
Alberto S. Cattaneo, Carlo A. Rossi
This paper analyzes in details the Batalin-Vilkovisky quantization procedure for BF theories on n-dimensional manifolds and describes a suitable superformalism to deal with the mas…
On a Vanishing Theorem of Kontsevich
Alberto S. Cattaneo, Giovanni Felder
This paper has been withdrawn by the authors, due a crucial mistake in Lemma 2
Loop observables for BF theories in any dimension and the cohomology of knots
Alberto S. Cattaneo, Paolo Cotta-Ramusino, Carlo A. Rossi
A generalization of Wilson loop observables for BF theories in any dimension is introduced in the Batalin-Vilkovisky framework. The expectation values of these observables are coho…
A path integral approach to the Kontsevich quantization formula
Alberto S. Cattaneo, Giovanni Felder
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…