Unexpected connections between Burnside Groups and Knot Theory

Abstract

In Classical Knot Theory and in the new Theory of Quantum Invariants substantial effort was directed toward the search for unknotting moves on links. We solve, in this note, several classical problems concerning unknotting moves. Our approach uses a new concept, Burnside groups of links, which establishes unexpected relationship between Knot Theory and Group Theory. Our method has the potential to be used in computational biology in the analysis of DNA via tangle embedding theory, as developed by D.W.Sumners.

11 pages, 9 figures

Cited by in corpus (9)

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• Remarks on Congruence of 3-manifolds
• Burnside groups and $n$-moves for links
• Generalized virtualization on welded links
• Ineffectiveness of homotopical invariants on Nakanishi's 4-move conjecture
• Milnor invariants, $2n$-moves and $V^n$-moves for welded string links