Knots, surfaces and complexity

Alina Vdovina (CUNY)

Abstract: Both Seifert and Tate knots are classical objects in knot theory. It may look quite rare for the same knot to share both of these properties. But we will show that most of alternating knots of given genus enjoy both of these properties and we call them Seifert-Tate knots. We will present explicit structure of Seifert-Tate knots and show low complexity of the isomorphism problem. The talk is based on joint papers with Olga Kharlampovich and Stephen Huggett.