Seongjeong Kim

collaborators

3 papers

math.GT2026

3-braids with 4-valent vertices and knot invariant

Seongjeong Kim, Vassily O. Manturov

We construct a picture-valued invariant of classical knots by using the group $G_{n}^{3}$ and the plat closure of braids. We introduce a modification of the group $G_{n}^{3}$ and define a…

math.GT2026

Secant-quandle: an invariant of braids and knots

Seongjeong Kim, Yangzhou Liu, Vassily Olegovich Manturov

We construct a novel invariant of braids and knots, secant-quandle (SQ),with generic secants serving as generators and generic horizontal trisecants serving as relations, i.e., $SQ…

math.GT2024

The groups $G_{n}^{k}$ and $2 n$ -gon tilings

Vassily Olegovich Manturov, Seongjeong Kim

In the present paper we discuss four ways of looking at rhombile tilings: stacking 3-dimensional cubes, elements of groups, and configurations of lines and points.

3-braids with 4-valent vertices and knot invariant

Secant-quandle: an invariant of braids and knots

The groups Gnk​ and 2n-gon tilings

The groups $G_{n}^{k}$ and $2 n$ -gon tilings