knot manifold
1Knot (mathematics) — A table of all prime knots with seven crossings or fewer (not including mirror images). In mathematics, a knot is an embedding of a circle in 3 dimensional Euclidean space, R3, considered up to continuous deformations (isotopies). A crucial… …
2Manifold — For other uses, see Manifold (disambiguation). The sphere (surface of a ball) is a two dimensional manifold since it can be represented by a collection of two dimensional maps. In mathematics (specifically in differential geometry and topology),… …
3Knot theory — A three dimensional depiction of a thickened trefoil knot, the simplest non trivial knot …
4Knot complement — In mathematics, the knot complement of a tame knot K is the set theoretic complement of the interior of the embedding of a solid torus into the 3 sphere. This solid torus is a thickened neighborhood of K . Note that the knot complement is a… …
5List of knot theory topics — 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 together so that it cannot be undone. In precise mathematical… …
63-manifold — In mathematics, a 3 manifold is a 3 dimensional manifold. The topological, piecewise linear, and smooth categories are all equivalent in three dimensions, so little distinction is usually made in whether we are dealing with say, topological 3… …
7History of knot theory — For thousands of years, knots have been used for basic purposes such as recording information, fastening and tying objects together. Over time people realized that different knots were better at different tasks, such as climbing or sailing. Knots …
8Figure-eight knot (mathematics) — In knot theory, a figure eight knot (also called Listing s knot) is the unique knot with a crossing number of four. This is the smallest possible crossing number except for the unknot and trefoil knot. Origin of name The name is given because… …
9Weeks manifold — In mathematics, the Weeks manifold, sometimes called the Fomenko Matveev Weeks manifold, is a closed hyperbolic 3 manifold obtained by (5,2) and (5,1) Dehn surgeries on the Whitehead link. It has volume approximately equal to .9427... and has the …
10Alternating knot — In knot theory, a link diagram is alternating if the crossings alternate under, over, under, over, as you travel along each component of the link. A link is alternating if it has an alternating diagram.Many of the knots with crossing number less… …
