Unexpected connections between Burnside Groups and Knot Theory

Details Unexpected connections between Burnside Groups and Knot Theory Unexpected connections between Burnside Groups and Knot Theory

2003-09-08

arxiv.org/abs/math/0309140v1

Mathematics

Geometric Topology

11 pages, 9 figures

Scientific paper

10.1073/pnas.0406098101

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.

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