Construction of holomorphic quilts in Cartesian product of closed surfaces
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 Lagrang...
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| Main Author | |
|---|---|
| Format | Journal Article |
| Language | English |
| Published |
29.09.2024
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| Subjects | |
| Online Access | Get full text |
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| Abstract | 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. |
|---|---|
| AbstractList | 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. |
| Author | Zhang, Zuyi |
| Author_xml | – sequence: 1 givenname: Zuyi surname: Zhang fullname: Zhang, Zuyi |
| BackLink | https://doi.org/10.48550/arXiv.2409.19744$$DView paper in arXiv |
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| Snippet | In this article, we modify the proof of holomorphic quilts from Wehrheim and
Woodward in \cite{wehrheim2009floer} to construct a specific type of immersed... |
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| SubjectTerms | Mathematics - Geometric Topology Mathematics - Symplectic Geometry |
| Title | Construction of holomorphic quilts in Cartesian product of closed surfaces |
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