Timeline for Embeddings of magnetic cotangent bundles over surfaces into closed symplectic 4-manifolds
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Oct 17, 2020 at 11:08 | comment | added | Tobias Diez | Thanks for the explanation. That construction works indeed, so you just silently suppressed the fiber resealing in your answer. | |
| Oct 16, 2020 at 12:01 | comment | added | Dmitri Panov | Tobias, you don't really need $t=1$ for this. The point is that if you consider a map from the cotangent bundle to itself that sends $\alpha\to t\alpha$, the canonical form $\omega$ pulls back to $t\omega$. So, any cotangent bundle with $\omega_{can}$ is simplectomorphic to one with $t\omega_{can}$. At the same time, this operation of scaling the fibers by $t$ doesn't affect the pullback of $\sigma$. Hopefully this answers your question. | |
| Oct 16, 2020 at 11:10 | comment | added | Tobias Diez | Why does $t \omega + \sigma'$ give you the magnetic form $\omega_{\textrm{can}} + \sigma$ on $U$ (seen as a subset of $T^* \Sigma$)? Don't you need $t = 1$ for this? | |
| Oct 16, 2020 at 1:57 | vote | accept | Rohil Prasad | ||
| Oct 15, 2020 at 20:42 | history | edited | Dmitri Panov | CC BY-SA 4.0 |
deleted 56 characters in body
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| Oct 15, 2020 at 20:22 | history | answered | Dmitri Panov | CC BY-SA 4.0 |