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unknotted circle

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  • 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 theory — A three dimensional depiction of a thickened trefoil knot, the simplest non trivial knot …   Wikipedia

  • Kirby calculus — In mathematics, the Kirby calculus in geometric topology is a method for modifying framed links in the 3 sphere using a finite set of moves, the Kirby moves. It is named for Robion Kirby. Using four dimensional Cerf theory, he proved that if M… …   Wikipedia

  • Whitehead manifold — In mathematics, the Whitehead manifold is an open 3 manifold that is contractible, but not homeomorphic to R3. Henry Whitehead discovered this puzzling object while he was trying to prove the Poincaré conjecture.A contractible manifold is one… …   Wikipedia

  • Alexander polynomial — In mathematics, the Alexander polynomial is a knot invariant which assigns a polynomial with integer coefficients to each knot type. James Waddell Alexander II discovered this, the first knot polynomial, in 1923. In 1969, John Conway showed a… …   Wikipedia

  • Torus knot — In knot theory, a torus knot is a special kind of knot which lies on the surface of an unknotted torus in R3. Similarly, a torus link is a link which lies on the surface of a torus in the same way. Each torus knot is specified by a pair of… …   Wikipedia

  • Exotic sphere — In differential topology, a mathematical discipline, an exotic sphere is a differentiable manifold M that is homeomorphic but not diffeomorphic to the standard Euclidean n sphere. That is, M is a sphere from the point of view of all its… …   Wikipedia

  • Lickorish–Wallace theorem — In mathematics, the Lickorish–Wallace theorem in the theory of 3 manifolds states that any closed, orientable, connected 3 manifold may be obtained by performing Dehn surgery on a framed link in the 3 sphere with +/ 1 surgery coefficients.… …   Wikipedia

  • knot theory — ▪ mathematics       in mathematics, the study of closed curves in three dimensions, and their possible deformations without one part cutting through another. Knots may be regarded as formed by interlacing and looping a piece of string in any… …   Universalium

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