Self-linking number

Self-linking number

In knot theory, the self-linking number is an invariant of framed knots. It is related to the linking number of curves.

A framing of a knot is a choice of a non-tangent vector at each point of the knot. Given a framed knot "C", the self-linking number is defined to be the linking number of "C" with a new curve obtained by pushing points of "C" along the framing vectors.

Given a Seifert surface for a knot, the associated Seifert framing is obtained by taking a tangent vector to the surface pointing inwards and perpendicular to the knot. The self-linking number obtained from a Seifert framing is always zero.

The blackboard framing of a knot is the framing where each of the vectors points in the vertical ("z") direction. The self-linking number obtained from the blackboard framing is called the Kauffman self-linking number of the knot. This is not a knot invariant because it is only well-defined up to regular isotopy.


Wikimedia Foundation. 2010.

Игры ⚽ Поможем решить контрольную работу

Look at other dictionaries:

  • Linking number — In mathematics, the linking number is a numerical invariant that describes the linking of two closed curves in three dimensional space. Intuitively, the linking number represents the number of times that each curve winds around the other. The… …   Wikipedia

  • Self-experimentation in medicine — Self experimentation refers to the very special case of single subject scientific experimentation in which the experimenter conducts the experiment on her or himself. Usually this means that the designer, operator, subject, analyst, and user or… …   Wikipedia

  • Wikipedia:Manual of Style/Linking — For technical information about link formatting, see Help:Link. For information on adding external links to articles, see Wikipedia:External links. Wikilinks redirects here. For the IRC script, see WP:Scripts/Wikilinks. This guideline is a part… …   Wikipedia

  • Winding number — The term winding number may also refer to the rotation number of an iterated map. This curve has winding number two around the point p. In mathematics, the winding number of a closed curve in the plane around a given point is an integer… …   Wikipedia

  • List of mathematics articles (S) — NOTOC S S duality S matrix S plane S transform S unit S.O.S. Mathematics SA subgroup Saccheri quadrilateral Sacks spiral Sacred geometry Saddle node bifurcation Saddle point Saddle surface Sadleirian Professor of Pure Mathematics Safe prime Safe… …   Wikipedia

  • Superhelix — A superhelix is a molecular structure in which a helix is itself coiled into a helix. This is significant to both proteins and genetic material, such as overwound circular DNA.The earliest significant reference in molecular biology is from 1971,… …   Wikipedia

  • Chern-Simons theory — The Chern Simons theory is a 3 dimensional topological quantum field theory of Schwarz type, developed by Shiing Shen Chern and James Harris Simons. In condensed matter physics, Chern Simons theory describes the topological orderin fractional… …   Wikipedia

  • Chern–Simons theory — The Chern–Simons theory is a 3 dimensional topological quantum field theory of Schwarz type, introduced by Edward Witten. It is so named because its action is proportional to the integral of the Chern–Simons 3 form. In condensed matter physics,… …   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

  • Reciprocity in network — A lot of theoretical efforts have been made to study the nontrivial properties of complex networks, such as clustering, scale free degree distribution, community structures, etc. Here Reciprocity is another quantity to specifically characterize… …   Wikipedia

Share the article and excerpts

Direct link
… Do a right-click on the link above
and select “Copy Link”