Legendrian

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• Legendrian knot — In mathematics, a Legendrian knot often refers to a smooth embedding of the circle into mathbb R^3, which is tangent to the standard contact structure on mathbb R^3. More generally, Legendrian knots refer to such maps into a contact manifold. ee… …   Wikipedia

• Contact geometry — Contact form redirects here. For a web email form, see Form (web)#Form to email scripts. The standard contact structure on R3. Each point in R3 has a plane associated to it by the contact structure, in this case as the kernel of the one form dz − …   Wikipedia

• Relative contact homology — In mathematics, in the area of symplectic topology, relative contact homology is an invariant of spaces together with a chosen subspace. Namely, it is associated to a contact manifold and one of its Legendrian submanifolds. It is a part of a more …   Wikipedia

• Dehn planes — In geometry, Dehn constructed two examples of planes, a semi Euclidean geometry and a non Legendrian geometry, that have infinitely many lines parallel to a given one that pass through a given point, but where the sum of the angles of a triangle… …   Wikipedia

• Thurston-Bennequin number — In knot theory, the Thurston Bennequin number, or Bennequin number, of a front diagram of a Legendrian knot is defined as the writhe of the diagram minus the number of right cusps. The maximum Thurston Bennequin number over all possible front… …   Wikipedia

• Lie sphere geometry — is a geometrical theory of planar or spatial geometry in which the fundamental concept is the circle or sphere. It was introduced by Sophus Lie in the nineteenth century. [The definitive modern textbook on Lie sphere geometry is Harvnb|Cecil|1992 …   Wikipedia

• Continuation map — In differential topology, given a family of Morse Smale functions on a smooth manifold X parameterized by a closed interval I, one can construct a Morse Smale vector field on X × I whose critical points occur only on the boundary. The Morse… …   Wikipedia

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

• List of mathematics articles (L) — NOTOC L L (complexity) L BFGS L² cohomology L function L game L notation L system L theory L Analyse des Infiniment Petits pour l Intelligence des Lignes Courbes L Hôpital s rule L(R) La Géométrie Labeled graph Labelled enumeration theorem Lack… …   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