Construction of holomorphic quilts in Cartesian product of closed surfaces
Abstract
In this article, we modify the proof of holomorphic quilts from Wehrheim and Woodward in wehrheim2009floer to construct a specific type of immersed holomorphic quilt, where the symplectic manifolds are closed surfaces. The application is to compare Lagrangian Floer theory with quilted Lagrangian Floer theory, as they relate through Lagrangian correspondence. A potential example is provided to support Bottman and Wehrheim's conjecture bottman2018gromov regarding the isomorphism between Lagrangian Floer homology and quilted Lagrangian Floer homology after twisting by bounding cochains.
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