Link diagrams with low Turaev genus

Abstract

We classify 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 closed curves 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.

21 pages, 35 figures

References in corpus (1)

• Turaev genus and alternating decompositions

Cited by in corpus (7)

• Turaev genus and alternating decompositions
• Invariants for Turaev genus one links
• Extremal Khovanov homology of Turaev genus one links
• A topological characterization of toroidally alternating knots
• On the Turaev genus of torus knots
• The Jones polynomial of an almost alternating link
• Geometric estimates from spanning surfaces