V. Manturov

activity

20242026

collaborators

8 papers

math.GT2026

Generalizations of the groups $G_{n}^{k}$ : graphs, moduli spaces, algebraic geometry, spherical braids

Vassily Olegovich Manturov

In this work, we construct a generalization of the $G_{n}^{k}$ -theory to the case of an arbitrary hypergraph. The case of spherical braids is considered separately, using the stratific…

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.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

A generalisation of the Burau representation and groups $G_{n}^{3}$ for classical braids

Vassily Olegovich Manturov, Igor Mikhailovich Nikonov

We consider a certain modification of the group $G_{n}^{3}$ which describes dynamics of point configurations, in particular braids, and define a representation of the modified $G_{n}^{3}$ .…

math.GT2025

Maps from knots to $2$ -links, chord diagrams, and a way to enhance Vassiliev invariants

Vassily Olegovich Manturov

In the present paper, we discuss a way of generalising Vassiliev knot invariants and weight systems to framed chord diagrams having framing 0 and 1.

math.GT2025

Shear coordinates and braid invariants

Vassily Olegovich Manturov

We present a way of using shear coordinates in hyperbolic geometry to get invariants of braids. This method also has a tropical analogue.

Generalizations of the groups Gnk​: graphs, moduli spaces, algebraic geometry, spherical braids

Secant-quandle: an invariant of braids and knots

3-braids with 4-valent vertices and knot invariant

A generalisation of the Burau representation and groups Gn3​ for classical braids

Maps from knots to 2-links, chord diagrams, and a way to enhance Vassiliev invariants

Shear coordinates and braid invariants

Generalizations of the groups $G_{n}^{k}$ : graphs, moduli spaces, algebraic geometry, spherical braids

A generalisation of the Burau representation and groups $G_{n}^{3}$ for classical braids

Maps from knots to $2$ -links, chord diagrams, and a way to enhance Vassiliev invariants