GEOMETRIC GENERATION OF THE WRAPPED FUKAYA CATEGORY OF WEINSTEIN MANIFOLDS AND SECTORS

Baptiste Chantraine (1) , Georgios Dimitroglou Rizell (2) , Paolo Ghiggini (1) , Roman Golovko (3)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 CAM - University of Cambridge [UK]
3 Département de mathématiques Université Libre de Bruxelles

We prove that the wrapped Fukaya category of any 2n-dimensional Weinstein manifold (or, more generally, Weinstein sector) W is generated by the unstable manifolds of the index n critical points of its Liouville vector field. Our proof is geometric in nature, relying on a surgery formula for Floer homology and the fairly simple observation that Floer homology vanishes for Lagrangian submanifolds that can be disjoined from the isotropic skeleton of the Weinstein manifold. Note that we do not need any additional assumptions on this skeleton. By applying our generation result to the diagonal in the product W × W , we obtain as a corollary that the open-closed map from the Hochschild homology of the wrapped Fukaya category of W to its symplectic coho-mology is an isomorphism, proving a conjecture of Seidel.

Domaines: Géométrie symplectique [math.SG]; Topologie géométrique [math.GT]; Géométrie différentielle [math.DG]

Baptiste Chantraine, Georgios Dimitroglou Rizell, Paolo Ghiggini, Roman Golovko. GEOMETRIC GENERATION OF THE WRAPPED FUKAYA CATEGORY OF WEINSTEIN MANIFOLDS AND SECTORS. 2018. ⟨hal-01873728⟩