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2021 Distinguishing open symplectic mapping tori via their wrapped Fukaya categories
Yusuf Barış Kartal
Geom. Topol. 25(3): 1551-1630 (2021). DOI: 10.2140/gt.2021.25.1551

Abstract

We present partial results towards a classification of symplectic mapping tori using dynamical properties of wrapped Fukaya categories. More precisely, we construct a symplectic manifold Tϕ associated to a Weinstein domain M, and an exact, compactly supported symplectomorphism ϕ. The symplectic manifold Tϕ is another Weinstein domain and its contact boundary is independent of ϕ. We distinguish Tϕ from T1M, under certain assumptions (Theorem 1.1). As an application, we obtain pairs of diffeomorphic Weinstein domains with the same contact boundary and whose symplectic cohomology groups are the same, as vector spaces, but that are different as Liouville domains. To our knowledge, this is the first example of such pairs that can be distinguished by their wrapped Fukaya category.

Previously, we have suggested a categorical model Mϕ for the wrapped Fukaya category W(Tϕ), and we have distinguished Mϕ from the mapping torus category of the identity. We prove W(Tϕ) and Mϕ are derived equivalent (Theorem 1.9); hence, deducing the promised Theorem 1.1. Theorem 1.9 is of independent interest as it preludes an algebraic description of wrapped Fukaya categories of locally trivial symplectic fibrations as twisted tensor products.

Citation

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Yusuf Barış Kartal. "Distinguishing open symplectic mapping tori via their wrapped Fukaya categories." Geom. Topol. 25 (3) 1551 - 1630, 2021. https://doi.org/10.2140/gt.2021.25.1551

Information

Received: 18 August 2019; Revised: 20 July 2020; Accepted: 22 August 2020; Published: 2021
First available in Project Euclid: 19 July 2021

Digital Object Identifier: 10.2140/gt.2021.25.1551

Subjects:
Primary: 53D37
Secondary: 16E45, 18G99, 53D40

Rights: Copyright © 2021 Mathematical Sciences Publishers

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Vol.25 • No. 3 • 2021
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