tame knot
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Knot 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… … Wikipedia
Knot (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… … Wikipedia
List 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… … Wikipedia
Framed knot — In the mathematical theory of knots, a framed knot is the extension of a tame knot to an embedding of the solid torus D 2 times; S 1 in S 3.The framing of the knot is the linking number of the image of the ribbon I times; S 1 with the knot. As… … Wikipedia
Wild knot — In the mathematical theory of knots, a knot is tame if it can be thickened up , that is, if there exists an extension to an embedding of the solid torus S 1 times; D 2 into the 3 sphere. A knot is tame if and only it can be represented as a… … Wikipedia
Racks and quandles — In mathematics, racks and quandles are sets with a binary operation satisfying axioms analogous to the Reidemeister moves of knot diagram manipulation.While studied primarily in a knot theoretic context, they can be viewed as algebraic… … Wikipedia
Eilenberg–Mazur swindle — In mathematics, the Eilenberg–Mazur swindle, named after Samuel Eilenberg and Barry Mazur, is a method of proof that involves paradoxical properties of infinite sums. In geometric topology it was introduced by Mazur (1959, 1961) and is often … Wikipedia
Small cancellation theory — In the mathematical subject of group theory, small cancellation theory studies groups given by group presentations satisfying small cancellation conditions, that is where defining relations have small overlaps with each other. It turns out that… … Wikipedia
Seifert surface — In mathematics, a Seifert surface is a surface whose boundary is a given knot or link. Such surfaces can be used to study the properties of the associated knot or link. For example, many knot invariants are most easily calculated using a Seifert… … Wikipedia
Braid group — In mathematics, the braid group on n strands, denoted by B n , is a certain group which has an intuitive geometrical representation, and in a sense generalizes the symmetric group S n . Here, n is a natural number; if n gt; 1, then B n is an… … Wikipedia
Nœud (mathématiques) — Une table de tous les nœuds premiers (en) ayant sept croisements … Wikipédia en Français
