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Joint Mathematical seminar of Saint Petersburg State University and Peking University
May 23, 2024 15:00–16:00, St. Petersburg, online
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Contact $+1$ surgeries and vanishing of contact homology
Zhengyi Zhouab a Morningside Center of Mathematics, Beijing
b Academy of Mathematics and Systems Science, Chinese Academy of Sciences
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Abstract:
From a surgical perspective, every contact manifold can be obtained from applying both isotropic and coisotropic surgeries on the standard contact sphere. Vanishing of contact homology, i.e. the incarnation of overtwistedness in symplectic field theory, can only arise from coisotropic surgeries, in particular, contact $+1$ surgeries. In this talk, I will explain situations of contact $+1$ surgeries yielding vanishing of contact homology both in dimension 3 and higher dimensions. In particular, I will explain contact $+1$ surgeries along any torus knots with maximal Thurston-Bennequin number produce tight contact manifolds with vanishing contact homology. This is partially joint with Youlin Li.
Language: English
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