Quantum Topology / Hopf Algebra Seminar
Eiji Ogasa
Meiji Gakuin University
Local Moves on Knots and Products of Knots
Abstract: Products of knots, producing a higher dimensional knot from two given knots (one of which is fibered), were defined by Kauffman and Neumann. We define and explain the knot product. Kauffman and Ogasa proved that if a 1- link J is obtained from a 1-link K by one crossing change (respectively, one crossing change), then the knot product of J and the Hopf link is obtained from that of K and it by one (3,3) pass move (resp. one twist move). They also proved a higher dimensional case. They proved that if a 2-link J is obtaied from a 2-link K by one ribbon move, then the knot product of J and the Hopf link is obtained from that of K and it by one (3,4)-pass move. They also proved a further higher dimensional case. The point of
this talk is to understand the interaction of generalized band passing moves with the action of the knot product.
Thursday February 22, 2018 at 3:00 PM in SEO 612