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Foliations with complex leaves

Giuliana Gigante, Giuseppe Tomassini (1993)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Let X be a smooth foliation with complex leaves and let D be the sheaf of germs of smooth functions, holomorphic along the leaves. We study the ringed space X , D . In particular we concentrate on the following two themes: function theory for the algebra D ⁢ X and cohomology with values in D .

Foreword

Bureš, J., Souček, V. (1994)

Proceedings of the Winter School "Geometry and Physics"

Foreword

Bureš, J., Souček, V. (1990)

Proceedings of the Winter School "Geometry and Physics"

Foreword

Bureš, J., Souček, V. (1996)

Proceedings of the Winter School "Geometry and Physics"

Foreword

Bureš, J., Souček, V. (1989)

Proceedings of the Winter School "Geometry and Physics"

Foreword

Bureš, J., Souček, V. (1987)

Proceedings of the Winter School "Geometry and Physics"

Foreword

Slovák, Jan (1996)

Proceedings of the 15th Winter School "Geometry and Physics"

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 · μ ) / K is compact for all μ . Then, we can define the “formal geometric quantization” of M as 𝒬 K - ∞ ( M ) : = ∑ μ ∈ K ^ 𝒬 ( M μ ) V μ K . The aim of this article is to study the functorial properties of the assignment ( M , K ) → 𝒬 K - ∞ ( M ) .

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).

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