|DATE||November 24 (Fri), 2017|
|TITLE||Link diagrams with low Turaev genus|
|ABSTRACT||In this talk, we will discuss classifications of link diagrams with Turaev genus one and two in terms of an alternating tangle structure of the link diagram.
The proof involves surgery along simple loops on the Turaev surface, called cutting loops, which have corresponding cutting arcs that are visible on the planar link diagram. These also provide new obstructions for a link diagram on a surface to come from the Turaev surface algorithm. We also show that inadequate Turaev genus one links are almost-alternating. If time remains, we will discuss recent progress based on this result and open problems.