Looking at two knots that each have, say, 11 crossings—the Conway knot in this case, and a closely related “mutant” knot called theKinoshita-Terasaka—knot theorists must try to answer a couple of key questions.Wolfram Alphaexplains: ...
Knotty problems - and real-world solutions: knot theory, once a math backwater, turns out to have applications that extend all the way to clinical medicine.Cipra, Barry
Knot Theory (1) Knotty Problems – Marc LackenbyfromUniversity of Oxford Number Theory (2) Numbers are Serious but they are also Fun – Michael AtiyahfromUniversity of Oxford Linear Diophantine equations and the extended Euclidean algorithm – 1st year student lecturefromUniversity of Oxford ...
In Classical Knot Theory and in the new Theory of Quantum Invariants\nsubstantial effort was directed toward the search for unknotting moves on\nlinks. We solve, in this note, several classical problems concerning unknotting\nmoves. Our approach uses a new concept, Burnside groups of links, ...
This paper is a survey of several papers in quandle homology theory and\ncocycle knot invariants that have been published recently. Here we describe\ncocycle knot invariants that are defined in a state-sum form, quandle homology,\nand methods of constructing non-trivial cohomology classes....
Knot Theory The mathematical study ofknots. Knot theory considers questions such as the following: 1. Given a tangled loop of string, is it really knotted or can it, with enough ingenuity and/or luck, be untangled without having to cut it?