32 relations: Alternating knot, Borromean rings, Colin Adams (mathematician), Connected space, Curvature, Dehn surgery, Figure-eight knot (mathematics), Hyperbolic 3-manifold, Hyperbolic Dehn surgery, Hyperbolic geometry, Hyperbolic volume, Knot complement, Link (knot theory), Mathematics, Perko pair, Prime knot, Riemannian manifold, Satellite knot, SnapPea, Split link, Stevedore knot (mathematics), The geometry and topology of three-manifolds, Three-twist knot, Topology (journal), Torus knot, William Menasco, William Thurston, (−2,3,7) pretzel knot, 3-sphere, 6₂ knot, 6₃ knot, 7₄ knot.
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 mathematics, the Borromean rings consist of three topological circles which are linked and form a Brunnian link (i.e., removing any ring results in two unlinked rings).
Colin Conrad Adams (born October 13, 1956) is a mathematician primarily working in the areas of hyperbolic 3-manifolds and knot theory.
In topology and related branches of mathematics, a connected space is a topological space that cannot be represented as the union of two or more disjoint nonempty open subsets.
In mathematics, curvature is any of a number of loosely related concepts in different areas of geometry.
In topology, a branch of mathematics, a Dehn surgery, named after Max Dehn, is a construction used to modify 3-manifolds.
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 mathematics, more precisely in topology and differential geometry, a hyperbolic 3–manifold is a manifold of dimension 3 equipped with a hyperbolic metric, that is a Riemannian metric which has all its sectional curvatures equal to -1.
In mathematics, hyperbolic Dehn surgery is an operation by which one can obtain further hyperbolic 3-manifolds from a given cusped hyperbolic 3-manifold.
In mathematics, hyperbolic geometry (also called Bolyai–Lobachevskian geometry or Lobachevskian geometry) is a non-Euclidean geometry.
In the mathematical field of knot theory, the hyperbolic volume of a hyperbolic link is the volume of the link's complement with respect to its complete hyperbolic metric.
In mathematics, the knot complement of a tame knot K is the three-dimensional space surrounding the knot.
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 the mathematical theory of knots, the Perko pair, named after Kenneth Perko, is a pair of entries in classical knot tables that actually represent the same knot.
In knot theory, a prime knot or prime link is a knot that is, in a certain sense, indecomposable.
In differential geometry, a (smooth) Riemannian manifold or (smooth) Riemannian space (M,g) is a real, smooth manifold M equipped with an inner product g_p on the tangent space T_pM at each point p that varies smoothly from point to point in the sense that if X and Y are differentiable vector fields on M, then p \mapsto g_p(X(p),Y(p)) is a smooth function.
In the mathematical theory of knots, a satellite knot is a knot that contains an incompressible, non boundary-parallel torus in its complement.
SnapPea is free software designed to help mathematicians, in particular low-dimensional topologists, study hyperbolic 3-manifolds.
In the mathematical field of knot theory, a split link is a link that has a (topological) 2-sphere in its complement separating one or more link components from the others.
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.
The geometry and topology of three-manifolds is a set of widely circulated but unpublished notes by William Thurston from 1978 to 1980 describing his work on 3-manifolds.
In knot theory, the three-twist knot is the twist knot with three-half twists.
Topology was a peer-reviewed mathematical journal covering topology and geometry.
In knot theory, a torus knot is a special kind of knot that lies on the surface of an unknotted torus in R3.
William W. Menasco is a topologist and a professor at the University at Buffalo.
William Paul Thurston (October 30, 1946August 21, 2012) was an American mathematician.
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.
In knot theory, the 62 knot is one of three prime knots with crossing number six, the others being the stevedore knot and the 63 knot.
In knot theory, the 63 knot is one of three prime knots with crossing number six, the others being the stevedore knot and the 62 knot.
In mathematical knot theory, 74 is the name of a 7-crossing knot which can be visually depicted in a highly-symmetric form, and so appears in the symbolism and/or artistic ornamentation of various cultures.