TL;DR
This paper introduces a new construction of the Fukaya-Seidel category for symplectic manifolds and extends it to three-manifolds using five-dimensional gauge theory, bridging symplectic geometry and gauge theory.
Contribution
It presents a novel construction of the Fukaya-Seidel category and extends it to three-manifolds via gauge theory, connecting symplectic and gauge theoretic frameworks.
Findings
New construction of Fukaya-Seidel category for symplectic manifolds
Extension of the category to three-manifolds using gauge theory
Establishment of a link between symplectic geometry and gauge theory
Abstract
Given a J-holomorphic Morse function on a symplectic manifold, a new construction of the Fukaya-Seidel category is outlined. Applying this construction in an infinite dimensional case, a Fukaya-Seidel-type category is associated to a smooth three-manifold. In this case the construction is based on a five-dimensional gauge theory.
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