Quantum Topology Seminar
Noboro Ito
National Institute of Technology, Ibaraki College, Japan
Finite type invariants filtered by forbidden moves for classical and virtual knots
Abstract: Unknotting operations are used to define filtered invariants
of classical and virtual knots. The original Vassiliev invariant is
defined using crossing change. We can also use virtual knot diagrams
and an operation called “Virtualization” to obtain filtered invariants
of virtual knots, called Gauss diagram formulas (Goussarov, Polyak,
and Viro, 2000). In our study, we showed that this filtration is
nontrivial for each degree. Further, we proposed a new filtered
invariant of virtual knots by using “forbidden move”. Here, we use
the fact that forbidden move is an unknotting operation (Kanenobu,
Nelson, independently, 2000) for virtual knots. This talk is based on
a joint work with Migiwa Sakurai (arXiv: 2008.02750).
Reference: N. Ito and M. Sakurai, arXiv: 2008.02750, published in J.
Math Soc. Japan (2019)
Thursday November 19, 2020 at 4:00 PM in Zoom