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.
| Identifer | oai:union.ndltd.org:columbia.edu/oai:academiccommons.columbia.edu:10.7916/d8-9xbk-hq04 |
| Date | January 2020 |
| Creators | Zhang, Zhongyi |
| Source Sets | Columbia University |
| Language | English |
| Detected Language | English |
| Type | Theses |
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