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Oct 18, 2017 at 17:37 comment added YHBKJ @ChiHongChow Handle cancellation does not change the Weinstein structure. Probably the following paper due to Casals-Murphy is a good reference for illustrating the real Morse theoretical view point of symplectic Lefschetz fibrations: arxiv.org/abs/1610.06977
Oct 18, 2017 at 9:39 comment added ChiHong Chow Thank you for your answers which indeed solved my question. In fact, I just wanted to see why $W$ is (the completion) of the standard symplectic ball. I have searched the key construction you mentioned, the stabilization, and I find the fact that after doing a stabilization, say we get $W'$ from $W$, the former is symplectomorphic to the latter. I would like to ask, how this symplectomorphism changes the Liouville structures? I don't know what this map looks like. I have just heard that it comes from the cancellation of two handlebodies. Thanks again.
Oct 18, 2017 at 9:18 vote accept ChiHong Chow
Oct 14, 2017 at 16:27 history answered YHBKJ CC BY-SA 3.0