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Construction of holomorphic quilts in Cartesian product of closed surfaces
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In this article, we modify the proof of holomorphic quilts from Wehrheim and Woodward in \cite{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 \cite{bottman2018gromov} regarding the isomorphism between Lagrangian Floer homology and quilted Lagrangian Floer homology after twisting by bounding cochains.
Forward citations
Cited by 2 Pith papers
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The instanton homology of the $(-2,3,q)$ pretzel knots and computed bounding cochains in the pillowcase
For every odd q≥3, the reduced singular instanton knot homology of P(-2,3,q) has rank q+2, and explicit pillowcase bounding cochains are computed that cancel or create one differential to match this rank.
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Equivalence of the pearly tree immersed Lagrangian Floer theory and the Hamiltonian immersed Lagrangian Floer theory
The pearly-tree and Hamiltonian immersed Lagrangian Floer chain groups are claimed to be canonically identified, extending Alston-Bao from the unobstructed to the obstructed setting.
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