### Seminars

### on knot theory and related topics

# Links in $S_{g} \times S^{1}$ and its lifting

Date:

Time:

15:30 (GMT +0)

Speaker:

Seongjeong Kim

Knots and representation theory (by Zoom)

Abstract: A virtual knot, which is one of generalizations of knots in $\mathbb{R}^{3}$ (or $S^{3}$), is, roughly speaking, an embedded circle in thickened surface $S_{g} \times I$. In this talk we will discuss about knots in 3 dimensional $S_{g} \times S^{1}$. We introduce basic notions for knots in $S_{g} \times S^{1}$, for example, diagrams, moves for diagrams and so on. For knots in $S_{g} \times S^{1}$ technically we lose over/under information, but we will have information how many times the knot rotates along $S^{1}$. We will discuss the geometric meaning of the rotating information.

ID: 818 6674 5751 Passcode: 141592