|Affiliation||Shanghai Jiao Tong University|
|Time||Jan 9 14:50~15:20|
|Title||The support genus of certain Legendrian knots|
A contact structure on an oriented 3-manifold is a maximally non-integrable plane distribution in the tangent bundle. Around 2000, Giroux established a one-to-one correspondence between the contact structures on an oriented 3-manifold and its open book decompositions in some sense. A Legendrian knot in a contact 3-manifold is a smooth knot which everywhere tangent to the contact plane distribution. For any Legendrian knot L in the standard contact structure in 3-sphere $S^3$, there is a correspondent open book decomposition one of whose pages contains $L$, such that the page framing of L agrees with the contact framing. The minimal genus of the pages of such open book decomposition is called, by Onaran and some others, the support genus of $L$. In this talk, we shall determine the support genus of all Legendrian right handed trefoil knots, some Legendrian torus knots, and some Legendrian twist knots. This answers a question of Onaran negatively. It is a joint work with Wang Jiajun.