cheatsheets:symplectic-contact-manifold
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| cheatsheets:symplectic-contact-manifold [2022/12/12 04:57] – [Linearized version] pzhou | cheatsheets:symplectic-contact-manifold [2023/06/25 15:53] (current) – external edit 127.0.0.1 | ||
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| ====== Symplectic and Contact manifolds ====== | ====== Symplectic and Contact manifolds ====== | ||
| + | Let's follow the reference of [[https:// | ||
| ===== Example of $\C$ ===== | ===== Example of $\C$ ===== | ||
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| Given an immersed Lagrangian $L$ in $W$ (no wrapping turned on) equipped with a potential, we can do the lift $L_+$ to $M$. Then, we have a free algebra generated by the double point in $L$, or Reeb chord ending in $L_+$. **It is hugely non-commutative**. The only thing makes geometric sense is the differential, | Given an immersed Lagrangian $L$ in $W$ (no wrapping turned on) equipped with a potential, we can do the lift $L_+$ to $M$. Then, we have a free algebra generated by the double point in $L$, or Reeb chord ending in $L_+$. **It is hugely non-commutative**. The only thing makes geometric sense is the differential, | ||
| - | So [[https:// | + | So [[https:// |
| ==== Linearized version ==== | ==== Linearized version ==== | ||
cheatsheets/symplectic-contact-manifold.1670821068.txt.gz · Last modified: 2023/06/25 15:53 (external edit)