Quantum Topology Seminar
Noboru Ito
National Institute of Technology, Ibaraki College, Japan
On a conjecture by Goussarov-Polyak-Viro for virtual knots and Gauss diagram formulas
Abstract:
A conjecture by Goussarov, Polyak, and Viro (arXiv:
math/9810073, published in Topology (2000)) has been still open:
Conjecture (Goussarov-Polyak-Viro 2000, Conjecture 3.C). Every
finite-type invariant of classical knots can be extended to a
finite-type invariant of long virtual knots.
For example, a well-known Polyak-Viro Gauss diagram formula (1994) of
finite degree three becomes a Vassiliev invariant of degree three for
classical knots whereas this formula cannot be directly obtained by a
“universal invariant” of virtual knots because this formula is not a
virtual knot invariant. In our study, we find a quotient module of
another version of Polyak algebra and this quotient implies the
Polyak-Viro formula. This talk is based on a joint work with Yuka
Kotorii (arXiv: 1905.01418).
Reference: N. Ito and Y. Kotorii, arXiv: 1905.01418
Thursday November 12, 2020 at 4:00 PM in Zoom