Displaying similar documents to “Obstructions to the existence of monotone Lagrangian embeddings into cotangent bundles of manifolds fibered over the circle”

An Algebraic Formula for the Index of a Vector Field on an Isolated Complete Intersection Singularity

H.-Ch. Graf von Bothmer, Wolfgang Ebeling, Xavier Gómez-Mont (2008)

Annales de l’institut Fourier

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Let ( V , 0 ) be a germ of a complete intersection variety in ℂ n + k , n > 0 , having an isolated singularity at 0 and X be the germ of a holomorphic vector field having an isolated zero at 0 and tangent to V . We show that in this case the homological index and the GSV-index coincide. In the case when the zero of X is also isolated in the ambient space ℂ n + k we give a formula for the homological index in terms of local linear algebra.

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 · 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 ) .

The tiered Aubry set for autonomous Lagrangian functions

Marie-Claude Arnaud (2008)

Annales de l’institut Fourier

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Let L : T M → ℝ be a Tonelli Lagrangian function (with M compact and connected and dim M ≥ 2 ). The tiered Aubry set (resp. Mañé set) 𝒜 T ( L ) (resp. 𝒩 T ( L ) ) is the union of the Aubry sets (resp. Mañé sets) 𝒜 ( L + λ ) (resp. 𝒩 ( L + λ ) ) for λ closed 1-form. Then the set 𝒩 T ( L ) is closed, connected and if dim H 1 ( M ) ≥ 2 , its intersection with any energy level is connected and chain...