Sectorial descent for wrapped Fukaya categories

Ganatra, Sheel; Pardon, J. F.; Shende, Vivek

doi:10.48550/arxiv.1809.03427

Cited by 30 publications

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“…where C σ k is the union of cocore disks of the top handles of X(σ k ), see Corollary 3.12. This colimit also follows from the more general sectorial descent result of Ganatra-Pardon-Shende [GPS18] on the level of wrapped Fukaya categories which is the motivating result for the present paper.…”

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confidence: 61%

“…Section 3 is devoted to the one-to-one correspondence between simplicial decompositions and good sectorial covers. In Section 3.2 we show that the main result in addition to the surgery formula of Bourgeois-Ekholm-Eliashberg recovers sectorial descent in wrapped Floer cohomology of Ganatra-Pardon-Shende [GPS18].…”

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confidence: 88%

“…Simplicial decompositions and good sectorial covers. We refer the reader to [GPS20,GPS18] for introduction and definitions of Weinstein sectors, sectorial covers and related notions. Definition 3.1 (Good sectorial cover).…”

Section: Good Sectorial Coversmentioning

confidence: 99%

“…One of the main results in [GPS18] says that there is a pre-triangulated equivalence of A ∞categories…”

Section: Good Sectorial Coversmentioning

confidence: 99%

“…Good sectorial covers. Let X = X 1 ∪ • • • ∪ X m be a sectorial cover of a Weinstein manifold in the sense of Ganatra-Pardon-Shende [GPS18]. We call the sectorial cover good if for any subset ∅ = A ⊂ {1, .…”

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confidence: 99%

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Simplicial descent for Chekanov-Eliashberg dg-algebras

Asplund¹

2021

Preprint

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We introduce a type of surgery decomposition of Weinstein manifolds we call simplicial decompositions. The main result of this paper is that the Chekanov-Eliashberg dg-algebra of the attaching spheres of a Weinstein manifold satisfies a descent (cosheaf) property with respect to a simplicial decomposition. Simplicial decompositions generalize the notion of Weinstein connected sum and we show that there is a one-to-one correspondence (up to Weinstein homotopy) between simplicial decompositions and so-called good sectorial covers. As an application we explicitly compute the Chekanov-Eliashberg dg-algebra of the Legendrian attaching spheres of a plumbing of copies of cotangent bundles of spheres of dimension at least three according to any plumbing quiver. We show by explicit computation that this Chekanov-Eliashberg dg-algebra is quasi-isomorphic to the Ginzburg dg-algebra of the plumbing quiver. Contents 19 3.1. Simplicial decompositions and good sectorial covers 19 3.2. Relation to sectorial descent 26 4. Applications 27 4.1. Legendrian submanifolds-with-boundary-and-corners 27 4.2. The Chekanov-Eliashberg cosheaf 30 4.3. Plumbing of cotangent bundles of spheres 31 References 36

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confidence: 61%

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confidence: 88%

Section: Good Sectorial Coversmentioning

confidence: 99%

“…One of the main results in [GPS18] says that there is a pre-triangulated equivalence of A ∞categories…”

Section: Good Sectorial Coversmentioning

confidence: 99%

mentioning

confidence: 99%

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Simplicial descent for Chekanov-Eliashberg dg-algebras

Asplund¹

2021

Preprint

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What is an equivalence in a higher category?

Ozornova,

Rovelli

2023

Bulletin of London Math Soc

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Symplectic flexibility and the Grothendieck group of the Fukaya category

Lazarev

2022

Journal of Topology

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In the previous work, the author used symplectic flexibility techniques to prove an upper bound on the number of generators of the wrapped Fukaya category of a high-dimensional, simply connected Weinstein domain. In this article, we give a purely categorical proof of this result for all Weinstein domains via Thomason's theorem on split-generating subcategories and the Grothendieck group. In the process, we prove that there is a surjective map from singular cohomology to the Grothendieck group of the Fukaya category, relate the acceleration map to symplectic cohomology and the Dennis trace map and upgrade Abouzaid's splitgeneration criterion to a generation criterion for Weinstein domains. As a geometric analog of Thomason's result, we also produce the first examples of exotic presentations for cotangent bundles as Weinstein handle attachments along infinitely many non-fillable Legendrians.

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Sectorial descent for wrapped Fukaya categories

Cited by 30 publications

References 0 publications

Simplicial descent for Chekanov-Eliashberg dg-algebras

Simplicial descent for Chekanov-Eliashberg dg-algebras

What is an equivalence in a higher category?

Symplectic flexibility and the Grothendieck group of the Fukaya category

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