On Knot Theoretical Counterpart of the Groups G^k_n

Explore a comprehensive lecture on knot theory and group theory presented by V. O. Manturov. Delve into the intricate connections between knots and groups, focusing on the counterpart of the groups G^k_n in knot theory. Learn about key concepts such as the tetrahedron relation, four community dirty relation, and general position relations. Examine various examples of groups, including permutation groups, and their relevance to geometry and topology. Investigate invariants, invisible generators, and classical generators in knot theory. Discover the North counterpart and the main features of this year's theory. Gain insights into the applications of group theory in knot diagrams and calculations. This 53-minute talk offers a deep dive into advanced topics in quantum topology, suitable for mathematicians and researchers interested in the intersection of knot theory and group theory.

Introduction
Main principle
Tetrahedron relation
Four community dirty relation
Examples of groups
What are groups
General position
General position relations
Permutation groups
Geometry and topology
Calculations
Invariants
Invisible generators
Classical generators
North counterpart
Theory of this year
Main feature
Drawing
Group theory