Invariants of Legendrian Knots from Open Book Decompositions

Date

2010-01-01

Author

Onaran, Sinem Celik

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

1
views

2
downloads

In this note, we define a new invariant of a Legendrian knot in a contact 3-manifold using an open book decomposition supporting the contact structure. We define the support genus sg(L) of a Legendrian knot L in a contact 3-manifold (M, xi) as the minimal genus of a page of an open book of M supporting the contact structure xi such that L sits on a page and the framings given by the contact structure and the page agree. We show that any null-homologous loose knot in an overtwisted contact structure has support genus zero. To prove this, we show that any topological link in any 3-manifold M sits on a page of a planar open book decomposition of M.

Subject Keywords

General Mathematics

URI

https://hdl.handle.net/11511/63754

Collections

Department of Mathematics, Article