Skip to Main content Skip to Navigation
Theses

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.
Complete list of metadatas

Cited literature [50 references]  Display  Hide  Download

https://tel.archives-ouvertes.fr/tel-02055565
Contributor : Abes Star :  Contact
Submitted on : Monday, March 4, 2019 - 9:59:06 AM
Last modification on : Wednesday, September 16, 2020 - 5:31:05 PM
Long-term archiving on: : Wednesday, June 5, 2019 - 12:56:49 PM

File

73157_MENNESSON_2018_diffusion...
Version validated by the jury (STAR)

Identifiers

  • HAL Id : tel-02055565, version 1

Citation

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

Share

Metrics

Record views

169

Files downloads

165