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In this note, we study formal deformations of derived representations of the principal series representations of $SL (2, ℝ)$ . In particular, we recover all the representations of the derived principal series by deforming one of them. Similar results are also obtained for $SL (2, ℂ)$ .

Formal deformations of symplectic manifolds with boundary.

Ryszard Nest, Boris Tsygan (1996)

Journal für die reine und angewandte Mathematik

Formal geometric quantization

Paul-Émile Paradan (2009)

Annales de l’institut Fourier

Let $K$ be a compact Lie group acting in a Hamiltonian way on a symplectic manifold $(M, Ω)$ which is pre-quantized by a Kostant-Souriau line bundle. We suppose here that the moment map $Φ$ is proper so that the reduced space $M_{μ} : = Φ^{- 1} (K \cdot μ) / K$ is compact for all $μ$ . Then, we can define the “formal geometric quantization” of $M$ as $𝒬_{K}^{- \infty} (M) : = \sum_{μ \in \hat{K}} 𝒬 (M_{μ}) V_{μ}^{K} .$ The aim of this article is to study the functorial properties of the assignment $(M, K) \to 𝒬_{K}^{- \infty} (M)$ .

Formal Lagrangian operad.

Cattaneo, Alberto S., Dherin, Benoit, Felder, Giovanni (2010)

International Journal of Mathematics and Mathematical Sciences

Formality and the Lefschetz property in symplectic and cosymplectic geometry

Giovanni Bazzoni, Marisa Fernández, Vicente Muñoz (2015)

Complex Manifolds

We review topological properties of Kähler and symplectic manifolds, and of their odd-dimensional counterparts, coKähler and cosymplectic manifolds. We focus on formality, Lefschetz property and parity of Betti numbers, also distinguishing the simply-connected case (in the Kähler/symplectic situation) and the b1 = 1 case (in the coKähler/cosymplectic situation).

Formality theorems: from associators to a global formulation

Gilles Halbout (2006)

Annales mathématiques Blaise Pascal

Let $M$ be a differential manifold. Let $Φ$ be a Drinfeld associator. In this paper we explain how to construct a global formality morphism starting from $Φ$ . More precisely, following Tamarkin’s proof, we construct a Lie homomorphism “up to homotopy" between the Lie algebra of Hochschild cochains on $C^{\infty} (M)$ and its cohomology $(Γ (M, Λ T M), {[-, -]}_{S}$ ). This paper is an extended version of a course given 8 - 12 March 2004 on Tamarkin’s works. The reader will find explicit examples, recollections on $G_{\infty}$ -structures, explanation of the...

Formazione di singolarità nel moto per curvatura media

Carlo Sinestrari (2001)

Bollettino dell'Unione Matematica Italiana

We study the formation of singularities for hypersurfaces evolving by mean curvature. After recalling the basic properties of the flow and the classical results about curves and convex surfaces, we give account of some recent developments of the theory for the case of surfaces with positive mean curvature. We show that for such surfaces we can obtain a–priori estimates on the principal curvatures which enable us to classify the singular profiles by the use of rescaling techniques.

Forme de contact sur la somme connexe de deux variétés de contact de dimension impaire

Christiane Meckert (1982)

Annales de l'institut Fourier

On donne une construction de formes de contact sur toute variété décomposable en somme connexe de variétés de contact en toute dimension.

Formes automorphes associées aux cycles géodésiques des surfaces de Riemann hyperboliques

Paul Gérardin (1980/1981)

Séminaire Bourbaki

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