Claremont Topology Seminar: Migiwa Sakurai (Shibaura Institute of Technology)

We welcome all undergraduate/graduate students and faculty to attend topology seminar!

Speaker: Migiwa Sakurai (Shibaura Institute of Technology)

Title: Clasp pass moves and arrow polynomials of virtual knots

Abstract: For classical knots, clasp pass moves are closely related to Vassiliev invariants of degree 3. Tsukamoto showed that the values of the Vassiliev invariant of degree 3 induced from the Jones polynomial for two knots differ by 0 or +36/-36, if they are related by a single clasp pass move. For virtual knots, the arrow polynomial is a generalization of the Jones polynomial and induces a Vassiliev invariant of degree 3. We show that the values of the Vassiliev invariant of degree 3 induced from the arrow polynomial of two virtual knots differ by 0 or +2304/-2304, if they are related by a single clasp pass move. We also obtain a lower bound of the distance between virtual knots by clasp pass moves.