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isotopic embedding

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  • Whitney embedding theorem — In mathematics, particularly in differential topology,there are two Whitney embedding theorems:*The strong Whitney embedding theorem states that any connected smooth m dimensional manifold (required also to be Hausdorff and second countable) can… …   Wikipedia

  • Homotopy — This article is about topology. For chemistry, see Homotopic groups. The two dashed paths shown above are homotopic relative to their endpoints. The animation represents one possible homotopy. In topology, two continuous functions from one… …   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

  • Surface — This article discusses surfaces from the point of view of topology. For other uses, see Differential geometry of surfaces, algebraic surface, and Surface (disambiguation). An open surface with X , Y , and Z contours shown. In mathematics,… …   Wikipedia

  • Torus — Not to be confused with Taurus (disambiguation). This article is about the surface and mathematical concept of a torus. For other uses, see Torus (disambiguation). A torus As the distance to th …   Wikipedia

  • Link (knot theory) — In mathematics, a link is a collection of knots which do not intersect, but which may be linked (or knotted) together. A knot can be described as a link with one component. Links and knots are studied in a branch of mathematics called knot theory …   Wikipedia

  • Problems in loop theory and quasigroup theory — In mathematics, especially abstract algebra, loop theory and quasigroup theory are active research areas with many open problems. As in other areas of mathematics, such problems are often made public at professional conferences and meetings. Many …   Wikipedia

  • Knot group — In mathematics, a knot is an embedding of a circle into 3 dimensional Euclidean space. The knot group of a knot K is defined as the fundamental group of the knot complement of K in R3,:pi 1(mathbb{R}^3 ackslash K).Two equivalent knots have… …   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

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