Negative Contact Surgery on Legendrian Non-simple Knot

Description of video

Date: 4/27/24
Speaker :Shunyu Wan

AGDT Seminar



    Abstract: Etnyre first asked the question on when contact surgery on distinct Legendrian knots produces distinct contact manifolds, and he showed that +1 contact surgeries on certain non Legendrian isotopic representatives of the twist knots always produce the same contact 3-manifold. However, later using linearized contact homology Bourgeois-Ekholm-Eliashberg showed that -1 contact surgery (Legendrian surgery) on those representatives of the twist knots will produce different contact 3-manifolds. Using the contact invariant and Legendrian LOSS invariant in Heegaard Floer theory we are able to show that any contact negative rational surgery (except -1) on the Legendrian representatives of  Legendrian representative of twist knots that have different LOSS invariants produces different contact manifolds with different contact invariants. I will first talk about the background on contact geometry and the statement of the problem/theorem, then I will talk about the proofs and how Heegaard Fleor came into play. This is joint work with Hugo Zhou. 


    Related videos


    Signature of Milnor fibers and map germs

    Roberto Giménez Conejero and Gergő Pintér

    AGDT Seminar

    on 4/28/23

    Moduli Theory and Singularities

    Kovács Sándor

    AGDT Seminar

    3 weeks, 2 days ago