Date/Time
Date(s) - 16/09/2025
7:00 pm - 8:00 pm

Speaker: Dr. Kodai Wada (Kobe University)

Location: Zoom

Title: The intersection polynomials of a long virtual knot

Abstract: The aim of this talk is to develop the study of long virtual knots by introducing twelve kinds of polynomial invariants called the intersection polynomials. We establish their some fundamental properties such as additivity under concatenation product, and provide a complete characterization of each of them. We also introduce two kinds of supporting genera of a long virtual knot as a new topological property, and describe a relationship between the supporting genera and intersection polynomials.
If time permits, we give a polynomial generalization of Goussarov-Poyak-Viro’s $v_{2,1}$- and $v_{2,2}$-invariants,
whose definition is based on that of the intersection polynomials.

This is joint work with Takuji Nakamura, Yasutaka Nakanishi and Shin Satoh.