Knot Theory

← Back to Domain-Specific Abstractions by Domain

9 domain-specific abstractions whose origin domain is Knot Theory.

• Bracket polynomial — A Laurent-polynomial state-sum invariant of framed unoriented link diagrams whose normalization yields the Jones polynomial for oriented links.
• HOMFLY polynomial — A two-variable oriented-link invariant defined by a skein relation and normalization that specializes to the Alexander and Jones polynomials.
• Knot invariant — A quantity, algebraic object or property assigned to a knot that is unchanged under the chosen knot-equivalence relation and can distinguish some inequivalent knots.
• Knot Polynomial — Compress a knot or link's ambient-isotopy class into a normalized polynomial or Laurent polynomial whose equality can obstruct nonequivalence, while never treating polynomial equality as a complete classification.
• Link (knot theory) — A finite disjoint union of smoothly or tamely embedded circles in three-dimensional space, considered up to ambient isotopy, with a knot as the one-component case.
• Link concordance — An equivalence between links whose components cobound disjoint embedded cylinders in one higher-dimensional spacetime.
• Linking number — An oriented integer invariant measuring how many times one disjoint closed curve winds around another in three-dimensional space.
• Torus knot — A knot isotopic to a closed curve winding p and q times around the two generating directions of an unknotted torus, with coprime p and q.
• Virtual knot — An equivalence class of knot diagrams with classical and virtual crossings under classical Reidemeister moves and virtual detour moves, equivalently knots in thickened surfaces up to stabilization.