中国科学院数学与系统科学研究院
数学研究所
数学科学全国重点实验室
拓扑研讨班
Speaker: Shunyu Wan (Georgia Tech)
Inviter: 李振坤
Language: Chinese
Title:Surgeries on knots and tight contact structures
Time & Venue: 2026年6月29日（星期一）14：30-15：30 & 南楼N820
Abstract:The existence and nonexistence of tight contact structures on 3-manifolds are interesting and important topics studied over the past thirty years. Etnyre-Honda found the first example of a 3-manifold that does not admit tight contact structures, and later Lisca-Stipsicz extended their result and showed that a Seifert fiber space admits a tight contact structure if and only if it is not smooth (2n-1)-surgery along the T(2,2n+1) torus knot for any positive integer n. Surprisingly, since then no other example of a 3-manifold without tight contact structures has been found. Hence, it is interesting to study if all such manifolds, except those mentioned above, admit a tight contact structure. Towards this goal, I will discuss the joint work with Zhenkun Li and Hugo Zhou about showing any negative surgeries on any knot in S^3 admit a tight contact structure.
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