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Homologie symplectique Tⁿ-équivariante pour les variétés toriques hamiltoniennes

Abstract : This thesis establishes the existence of a version of Floer homology in a Morse-Bottcontext. Given a toric manifold (Wⁿ, ω, µ) and a hamiltonian H : W × S¹ → ℝ invariant bythe action of the torus Tⁿ, the periodical orbits of H are stable by the toric action.The latter admits fix points in W and hence it not free, neither one induced on the spaceof the loops of W and it is, a priori, impossible to establish a equivariant infinite-dimensionalMorse-Bott theory on C∞(S¹, W)/Tⁿ. We deal with this problem using Borel’s construction : we choose a space contractible E witha free action from the torus and look at the infinite-dimensional Morse-Bott homology of thespace (C∞(S¹, W) × E)/Tⁿ where Tⁿ act in a diagonal way on the product.We obtain an invariant for symplectic toric manifold and computes it for a closed manifold.
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Submitted on : Monday, March 4, 2019 - 9:59:06 AM
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  • HAL Id : tel-02055565, version 1


Pierre Mennesson. Homologie symplectique Tⁿ-équivariante pour les variétés toriques hamiltoniennes. Géométrie différentielle [math.DG]. Université Paris-Saclay, 2018. Français. ⟨NNT : 2018SACLS315⟩. ⟨tel-02055565⟩



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