Table of Contents
36 relations: Abelian group, Alexander polynomial, Andrew Casson, Ball (mathematics), Boundary (topology), Cameron Gordon (mathematician), Chiral knot, Cone (topology), Conway knot, Embedding, Equivalence relation, Figure-eight knot, Genus (mathematics), Homomorphism, Integer, Invertible knot, John Horton Conway, John Milnor, Knot (mathematics), Laurent polynomial, Lisa Piccirillo, Local flatness, Morse theory, Mutation (knot theory), Order (group theory), Peter Teichner, Prime knot, Ralph Fox, Ribbon knot, Signature of a knot, Slice genus, Smoothness, Stevedore knot (mathematics), Trefoil knot, Twist knot, 3-sphere.
- Slice knots and links
Abelian group
In mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written.
See Slice knot and Abelian group
Alexander polynomial
In mathematics, the Alexander polynomial is a knot invariant which assigns a polynomial with integer coefficients to each knot type.
See Slice knot and Alexander polynomial
Andrew Casson
Andrew John Casson FRS (born 1943) is a mathematician, studying geometric topology.
See Slice knot and Andrew Casson
Ball (mathematics)
In mathematics, a ball is the solid figure bounded by a sphere; it is also called a solid sphere.
See Slice knot and Ball (mathematics)
Boundary (topology)
In topology and mathematics in general, the boundary of a subset of a topological space is the set of points in the closure of not belonging to the interior of.
See Slice knot and Boundary (topology)
Cameron Gordon (mathematician)
Cameron Gordon (born 1945) is a Professor and Sid W. Richardson Foundation Regents Chair in the Department of Mathematics at the University of Texas at Austin, known for his work in knot theory.
See Slice knot and Cameron Gordon (mathematician)
Chiral knot
In the mathematical field of knot theory, a chiral knot is a knot that is not equivalent to its mirror image (when identical while reversed).
See Slice knot and Chiral knot
Cone (topology)
In topology, especially algebraic topology, the cone of a topological space X is intuitively obtained by stretching X into a cylinder and then collapsing one of its end faces to a point.
See Slice knot and Cone (topology)
Conway knot
In mathematics, in particular in knot theory, the Conway knot (or Conway's knot) is a particular knot with 11 crossings, named after John Horton Conway. Slice knot and Conway knot are slice knots and links.
See Slice knot and Conway knot
Embedding
In mathematics, an embedding (or imbedding) is one instance of some mathematical structure contained within another instance, such as a group that is a subgroup.
Equivalence relation
In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive.
See Slice knot and Equivalence relation
Figure-eight knot
The figure-eight knot or figure-of-eight knot is a type of stopper knot.
See Slice knot and Figure-eight knot
Genus (mathematics)
In mathematics, genus (genera) has a few different, but closely related, meanings.
See Slice knot and Genus (mathematics)
Homomorphism
In algebra, a homomorphism is a structure-preserving map between two algebraic structures of the same type (such as two groups, two rings, or two vector spaces).
See Slice knot and Homomorphism
Integer
An integer is the number zero (0), a positive natural number (1, 2, 3,...), or the negation of a positive natural number (−1, −2, −3,...). The negations or additive inverses of the positive natural numbers are referred to as negative integers.
Invertible 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.
See Slice knot and Invertible knot
John Horton Conway
John Horton Conway (26 December 1937 – 11 April 2020) was an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory.
See Slice knot and John Horton Conway
John Milnor
John Willard Milnor (born February 20, 1931) is an American mathematician known for his work in differential topology, algebraic K-theory and low-dimensional holomorphic dynamical systems.
See Slice knot and John Milnor
Knot (mathematics)
In mathematics, a knot is an embedding of the circle into three-dimensional Euclidean space, (also known as). Often two knots are considered equivalent if they are ambient isotopic, that is, if there exists a continuous deformation of which takes one knot to the other.
See Slice knot and Knot (mathematics)
Laurent polynomial
In mathematics, a Laurent polynomial (named after Pierre Alphonse Laurent) in one variable over a field \mathbb is a linear combination of positive and negative powers of the variable with coefficients in \mathbb.
See Slice knot and Laurent polynomial
Lisa Piccirillo
Lisa Marie Piccirillo (born 1990 or 1991)The Boston Globe, August 20, 2020; print title: "A Tough Knot to Crack," The Boston Globe Magazine (August 23, 2020), pp.
See Slice knot and Lisa Piccirillo
Local flatness
In topology, a branch of mathematics, local flatness is a smoothness condition that can be imposed on topological submanifolds.
See Slice knot and Local flatness
Morse theory
In mathematics, specifically in differential topology, Morse theory enables one to analyze the topology of a manifold by studying differentiable functions on that manifold.
See Slice knot and Morse theory
Mutation (knot theory)
In the mathematical field of knot theory, a mutation is an operation on a knot that can produce different knots.
See Slice knot and Mutation (knot theory)
Order (group theory)
In mathematics, the order of a finite group is the number of its elements.
See Slice knot and Order (group theory)
Peter Teichner
Peter Teichner (born June 30, 1963 in Bratislava, Czechoslovakia) is a German mathematician and one of the directors of the Max Planck Institute for Mathematics in Bonn.
See Slice knot and Peter Teichner
Prime knot
In knot theory, a prime knot or prime link is a knot that is, in a certain sense, indecomposable.
Ralph Fox
Ralph Hartzler Fox (March 24, 1913 – December 23, 1973) was an American mathematician.
Ribbon knot
In the mathematical area of knot theory, a ribbon knot is a knot that bounds a self-intersecting disk with only ribbon singularities. Slice knot and ribbon knot are slice knots and links.
See Slice knot and Ribbon knot
Signature of a knot
The signature of a knot is a topological invariant in knot theory.
See Slice knot and Signature of a knot
Slice genus
In mathematics, the slice genus of a smooth knot K in S3 (sometimes called its Murasugi genus or 4-ball genus) is the least integer g such that K is the boundary of a connected, orientable 2-manifold S of genus g properly embedded in the 4-ball D4 bounded by S3.
See Slice knot and Slice genus
Smoothness
In mathematical analysis, the smoothness of a function is a property measured by the number, called differentiability class, of continuous derivatives it has over its domain.
Stevedore knot (mathematics)
In knot theory, the stevedore knot is one of three prime knots with crossing number six, the others being the 62 knot and the 63 knot. Slice knot and stevedore knot (mathematics) are slice knots and links.
See Slice knot and Stevedore knot (mathematics)
Trefoil knot
In knot theory, a branch of mathematics, the trefoil knot is the simplest example of a nontrivial knot. Slice knot and trefoil knot are slice knots and links.
See Slice knot and Trefoil knot
Twist knot
In knot theory, a branch of mathematics, a twist knot is a knot obtained by repeatedly twisting a closed loop and then linking the ends together.
3-sphere
In mathematics, a 3-sphere, glome or hypersphere is a higher-dimensional analogue of a sphere.
See also
Slice knots and links
- Conway knot
- Kinoshita–Terasaka knot
- Ribbon knot
- Slice knot
- Square knot (mathematics)
- Stevedore knot (mathematics)
- Trefoil knot
- Unknot
References
Also known as Slice (topology), Sliceness, Topologically slice.