A survey on the Turaev genus of knots

Understand

The Turaev genus of a knot is a topological measure of how far a given knot is from being alternating.

• Recent work by several authors has focused attention on this interesting invariant.
• We discuss how the Turaev genus is related to other knot invariants, including the Jones polynomial, knot homology theories, and ribbon-graph polynomial invariants.