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On Wrapped Fukaya Category and loop space of Lagrangians in a Liouville Manifold

Zhang, Zhongyi

We introduce an $A_\infty$ map from the cubical chain complex of the based loop space of Lagrangian submanifolds with Legendrian boundary in a Liouville Manifold $C_{*}(\Omega_{L} \Lag)$ to wrapped Floer cohomology of Lagrangian submanifold $\CW^{-*}(L,L)$. In the case of a cotangent bundle and a Lagrangian co-fiber, the composition of our map with the map from $\CW^{-*}(L,L) \to C_{*}(\Omega_q Q) $ as defined in \cite{Ab12} shows that this map is split surjective.

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More About This Work

Academic Units
Mathematics
Thesis Advisors
Abouzaid, Mohammed
Degree
Ph.D., Columbia University
Published Here
July 6, 2020