Name  Sungmo Kang 

Affiliation  University of Quebec at Montreal 
Talk type  Session 
Time  Jan 10 14:50~15:20 
Location  E11101 
Title  The primitive/primitive and primitive/Seifert knot in $S^3$. 
Abstract 
Let $k$ be a simple closed curve in a genus two Heegaard surface
$\Sigma$ of $S^3$ bounding handlebodies $H$ and $H'$. $k$ is
called a primitive/primitive or doubleprimitive curve if adding a 2handle to $H$ and
$H'$ yields a solid torus. Similarly $k$ is called a primitive/Seifert curve if adding a 2handle to ,say, $H$ and $H'$ yields a solid torus and a Seifertfibered space respectively.
Primitive/primitive and primitive/Seifert curves are of some interest because they have
Dehn surgeries which yield lens spaces and Seifertfibered spaces respectively.
In this talk, I will explain how to find all primitive/primitive and primitive/Seifert knots in $S^3$ and how these have been grouped into the complete list of all such knots. The main tool for the classification uses RR diagrams together with the fact that if adding a 2handle to a genus two handlebody $H$ along a nonspearating curve $R$ on $\partial H$ embeds in $S^3$ as a knot exterior, then the meridian of the knot exterior can be obtained by surgery on $R$ along a wave. This is joint work with John Berge.

Slide  101110/PPPSF_talk.pdf 