Geometric generation of the wrapped Fukaya category of Weinstein manifolds and sectors
By Baptiste Chantraine, Georgios Dimitroglou Rizell, P. Ghiggini, R. Golovko. Annales Scientifiques de l'Ecole Normale Supérieure, 2017
74 citations recorded by the source corpus.
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 $W \times W$, we obtain as a corollary that the open-closed map from the Hochschild homology of the wrapped Fukaya category of $W$ to its symplectic homology is an isomorphism, proving a conjecture of Seidel.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/133bbc5c72e3218703baa06b8a5081118f0a13da
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In Geometry and Topology
- Vivek V. Shende
- J. Pardon
- Sheel Ganatra
- Roger Casals
- Honghao Gao
- Zachary Sylvan
- Nick Sheridan
- I. Smith
In Mathematical Physics
- J. Pardon
- Vivek V. Shende
- Sheel Ganatra
- Roger Casals
- Honghao Gao
- Zachary Sylvan
- Nick Sheridan
- I. Smith
Citations in the corpus
- Sectorial descent for wrapped Fukaya categories (2018, methodology): “The case of Theorem 1.10 in which f admits a Weinstein ribbon (compare Remark 1.7) was recently proven independently by Chantraine–Dimitroglou Rizell–Ghiggini–Golovko [12].3 This generation result for Weinstein manifolds has long been expected (see Bourgeois– Ekholm–Eliashberg [11] and the discussio”
- Infinitely many Lagrangian fillings (2020, background): “The wrapped Fukaya categories of the Weinstein manifolds M(n,m) are generated by their respective unique cocore C of their defining 2-handle [1, 15], i.”