Geometry seminar - Surgeries on knots and tight contact structures
Speaker:
Shunyu Wan (Georgia Institute of Technology)
Time:
August 10, 3-4pm
Location:
HIMIS 7A1
Title:
Surgeries on knots and tight contact structures
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.
Bio:
Shunyu Wan is a Visiting Assistant Professor at Georgia Institute of Technology. He got his PhD from University of Virginia, under supervision of Professor Tom Mark. His research area focus mainly on 3 and 4 dimensional topology, Heegaard Floer homology, symplectic and contact topology.