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arXiv · 1803.07676

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

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?

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James Pascaleff. 2018-03-20. Poisson geometry, monoidal Fukaya categories, and commutative Floer cohomology rings. https://arxiv.org/abs/1803.07676

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