Search results
Results from the WOW.Com Content Network
This record motivated the early knot theorists, but knot theory eventually became part of the emerging subject of topology. These topologists in the early part of the 20th century— Max Dehn , J. W. Alexander , and others—studied knots from the point of view of the knot group and invariants from homology theory such as the Alexander polynomial .
In 1992, the Journal of Knot Theory and Its Ramifications was founded, establishing a journal devoted purely to knot theory. In the early 1990s, knot invariants which encompass the Jones polynomial and its generalizations, called the finite type invariants, were discovered by Vassiliev and Goussarov.
Knot theory is the study of mathematical knots. While inspired by knots which appear in daily life in shoelaces and rope, a mathematician's knot differs in that the ends are joined so that it cannot be undone. In precise mathematical language, a knot is an embedding of a circle in 3-dimensional Euclidean space, R 3.
Knot theory is a branch of topology that concerns itself with abstract properties of mathematical knots — the spatial arrangements that in principle could be assumed by a closed loop of string. The main article for this category is Knot theory .
In knot theory, prime knots are those knots that are indecomposable under the operation of knot sum. The prime knots with ten or fewer crossings are listed here for quick comparison of their properties and varied naming schemes.
The prime Kinoshita–Terasaka knot (11n42) and the prime Conway knot (11n34) respectively, and how they are related by mutation. In the mathematical field of knot theory, a mutation is an operation on a knot that can produce different knots. Suppose K is a knot given in the form of a knot diagram.
Trefoil knot without 3-fold symmetry being unknotted by one crossing switch. Whitehead link being unknotted by undoing one crossing. In the mathematical area of knot theory, the unknotting number of a knot is the minimum number of times the knot must be passed through itself (crossing switch) to untie it.
A reduced diagram is one in which all the isthmi are removed. Tait came up with his conjectures after his attempt to tabulate all knots in the late 19th century. As a founder of the field of knot theory, his work lacks a mathematically rigorous framework, and it is unclear whether he intended the conjectures to apply to all knots, or just to alternating knots.