23 relations: Alexander polynomial, Algebraic geometry, Cone (topology), Cusp (singularity), Figure-eight knot (mathematics), Hopf link, Knot (mathematics), Knot theory, Link (knot theory), Mathematics, Milnor map, Open book decomposition, Plane curve, Seifert surface, Singular point of a curve, Singularity (mathematics), Stevedore knot (mathematics), Trefoil knot, Twist knot, Unit circle, Unknot, (−2,3,7) pretzel knot, 3-sphere.
In mathematics, the Alexander polynomial is a knot invariant which assigns a polynomial with integer coefficients to each knot type.
Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials.
In topology, especially algebraic topology, the cone CX of a topological space X is the quotient space: of the product of X with the unit interval I.
In mathematics a cusp, sometimes called spinode in old texts, is a point on a curve where a moving point on the curve must start to move backward.
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 mathematical knot theory, the Hopf link is the simplest nontrivial link with more than one component.
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 topology, knot theory is the study of mathematical knots.
In mathematical knot theory, a link is a collection of knots which do not intersect, but which may be linked (or knotted) together.
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
In mathematics, Milnor maps are named in honor of John Milnor, who introduced them to topology and algebraic geometry in his book Singular Points of Complex Hypersurfaces (Princeton University Press, 1968) and earlier lectures.
In mathematics, an open book decomposition (or simply an open book) is a decomposition of a closed oriented 3-manifold M into a union of surfaces (necessarily with boundary) and solid tori.
In mathematics, a plane curve is a curve in a plane that may be either a Euclidean plane, an affine plane or a projective plane.
In mathematics, a Seifert surface (named after German mathematician Herbert Seifert) is a surface whose boundary is a given knot or link.
In geometry, a singular point on a curve is one where the curve is not given by a smooth embedding of a parameter.
In mathematics, a singularity is in general a point at which a given mathematical object is not defined, or a point of an exceptional set where it fails to be well-behaved in some particular way, such as differentiability.
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.
In topology, a branch of mathematics, the trefoil knot is the simplest example of a nontrivial 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.
In mathematics, a unit circle is a circle with a radius of one.
The unknot arises in the mathematical theory of knots.
In geometric topology, a branch of mathematics, the (−2, 3, 7) pretzel knot, sometimes called the Fintushel–Stern knot (after Ron Fintushel and Ronald J. Stern), is an important example of a pretzel knot which exhibits various interesting phenomena under three-dimensional and four-dimensional surgery constructions.
In mathematics, a 3-sphere, or glome, is a higher-dimensional analogue of a sphere.