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Mathematics > Symplectic Geometry

arXiv:1803.07676 (math)
[Submitted on 20 Mar 2018 (v1), last revised 6 Jun 2023 (this version, v5)]

Title:Poisson geometry, monoidal Fukaya categories, and commutative Floer cohomology rings

Authors:James Pascaleff
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Abstract:We describe connections between concepts arising in Poisson geometry and the theory of Fukaya categories. The key concept is that of a symplectic groupoid, which is an integration of a Poisson manifold. The Fukaya category of a symplectic groupoid is monoidal, and it acts on the Fukaya categories of the symplectic leaves of the Poisson structure. Conversely, we consider a wide range of known monoidal structures on Fukaya categories and observe that they all arise from symplectic groupoids. We also use the picture developed to resolve a conundrum in Floer theory: why are some Lagrangian Floer cohomology rings commutative?
Comments: v5: Revised discussion of tensor products. 28 pages + 16-page Appendix
Subjects: Symplectic Geometry (math.SG)
MSC classes: 53D17, 53D37, 53D40
Cite as: arXiv:1803.07676 [math.SG]
  (or arXiv:1803.07676v5 [math.SG] for this version)
  https://doi.org/10.48550/arXiv.1803.07676

Submission history

From: James Pascaleff [view email]
[v1] Tue, 20 Mar 2018 22:11:01 UTC (28 KB)
[v2] Wed, 8 Aug 2018 15:48:48 UTC (29 KB)
[v3] Thu, 13 Jan 2022 15:57:37 UTC (53 KB)
[v4] Fri, 3 Feb 2023 17:23:09 UTC (58 KB)
[v5] Tue, 6 Jun 2023 15:02:58 UTC (60 KB)
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