23 relations: Alexander polynomial, Alternating knot, Ambient isotopy, Chirality (mathematics), Crossing number (knot theory), Figure-eight knot (mathematics), Homeomorphism, HOMFLY polynomial, Invertible knot, Jones polynomial, Knot (mathematics), Knot invariant, Knot theory, Mathematics, Max Dehn, Morwen Thistlethwaite, On-Line Encyclopedia of Integer Sequences, Orientability, Peter Tait (physicist), Prime knot, Torus knot, Trefoil knot, 3-sphere.
In mathematics, the Alexander polynomial is a knot invariant which assigns a polynomial with integer coefficients to each knot type.
In knot theory, a knot or link diagram is alternating if the crossings alternate under, over, under, over, as one travels along each component of the link.
In the mathematical subject of topology, an ambient isotopy, also called an h-isotopy, is a kind of continuous distortion of an ambient space, for example a manifold, taking a submanifold to another submanifold.
In geometry, a figure is chiral (and said to have chirality) if it is not identical to its mirror image, or, more precisely, if it cannot be mapped to its mirror image by rotations and translations alone.
In the mathematical area of knot theory, the crossing number of a knot is the smallest number of crossings of any diagram of the knot.
In knot theory, a figure-eight knot (also called Listing's knot or a Cavendish knot) is the unique knot with a crossing number of four.
In the mathematical field of topology, a homeomorphism or topological isomorphism or bi continuous function is a continuous function between topological spaces that has a continuous inverse function.
In the mathematical field of knot theory, the HOMFLY polynomial, sometimes called the HOMFLY-PT polynomial or the generalized Jones polynomial, is a 2-variable knot polynomial, i.e. a knot invariant in the form of a polynomial of variables m and l. A central question in the mathematical theory of knots is whether two knot diagrams represent the same knot.
In mathematics, especially in the area of topology known as knot theory, an invertible knot is a knot that can be continuously deformed to itself, but with its orientation reversed.
In the mathematical field of knot theory, the Jones polynomial is a knot polynomial discovered by Vaughan Jones in 1984.
In mathematics, a knot is an embedding of a circle S^1 in 3-dimensional Euclidean space, R3 (also known as E3), considered up to continuous deformations (isotopies).
In the mathematical field of knot theory, a knot invariant is a quantity (in a broad sense) defined for each knot which is the same for equivalent knots.
In topology, knot theory is the study of mathematical knots.
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
Max Wilhelm Dehn (November 13, 1878 – June 27, 1952) was a German-born American mathematician and student of David Hilbert.
Morwen B. Thistlethwaite is a knot theorist and professor of mathematics for the University of Tennessee in Knoxville.
The On-Line Encyclopedia of Integer Sequences (OEIS), also cited simply as Sloane's, is an online database of integer sequences.
In mathematics, orientability is a property of surfaces in Euclidean space that measures whether it is possible to make a consistent choice of surface normal vector at every point.
Peter Guthrie Tait FRSE (28 April 1831 – 4 July 1901) was a Scottish mathematical physicist and early pioneer in thermodynamics.
In knot theory, a prime knot or prime link is a knot that is, in a certain sense, indecomposable.
In knot theory, a torus knot is a special kind of knot that lies on the surface of an unknotted torus in R3.
In topology, a branch of mathematics, the trefoil knot is the simplest example of a nontrivial knot.
In mathematics, a 3-sphere, or glome, is a higher-dimensional analogue of a sphere.
Achiral knot, Amphicheiral knot, Amphichiral knot, Amphichiral link, Chiral link, Chirality (knot theory), Fully amphichiral knot, Fully amphichiral link, Knot chirality, Knot symmetry, Negative amphichiral knot, Positive amphichiral knot, Reversible knot, Reversible link.