Moment maps and geometric invariant theory

Chris Woodward

Displaying similar documents to “Moment maps and geometric invariant theory”

Moment maps and geometric invariant theory—Corrected version (October 2011)

Chris Woodward (2010)

Les cours du CIRM

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Symplectic torus actions with coisotropic principal orbits

Johannes Jisse Duistermaat, Alvaro Pelayo (2007)

Annales de l’institut Fourier

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In this paper we completely classify symplectic actions of a torus $T$ on a compact connected symplectic manifold $(M, σ)$ when some, hence every, principal orbit is a coisotropic submanifold of $(M, σ)$ . That is, we construct an explicit model, defined in terms of certain invariants, of the manifold, the torus action and the symplectic form. The invariants are invariants of the topology of the manifold, of the torus action, or of the symplectic form. In order to deal with symplectic actions...

Singular reduction of generalized complex manifolds.

Goldberg, Timothy E. (2010)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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Homotopy theory and circle actions on symplectic manifolds

John Oprea (1998)

Banach Center Publications

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Formal geometric quantization

Paul-Émile Paradan (2009)

Annales de l’institut Fourier

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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 $(M, K) \to 𝒬_{K}^{- \infty} (M)$ .

Induced differential forms on manifolds of functions

Cornelia Vizman (2011)

Archivum Mathematicum

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Differential forms on the Fréchet manifold $ℱ (S, M)$ of smooth functions on a compact $k$ -dimensional manifold $S$ can be obtained in a natural way from pairs of differential forms on $M$ and $S$ by the hat pairing. Special cases are the transgression map $Ω^{p} (M) \to Ω^{p - k} (ℱ (S, M))$ (hat pairing with a constant function) and the bar map $Ω^{p} (M) \to Ω^{p} (ℱ (S, M))$ (hat pairing with a volume form). We develop a hat calculus similar to the tilda calculus for non-linear Grassmannians [6].