|
Quantum Invariants
In the mathematical field of knot theory, a quantum knot invariant or quantum invariant of a knot (mathematics), knot or link is a linear sum of Jones polynomial#Colored Jones polynomial, colored Jones polynomial of Surgery theory, surgery presentations of the knot complement. List of invariants *Finite type invariant *Kontsevich invariant *Volume conjecture, Kashaev's invariant *Chern–Simons theory, Witten–Reshetikhin–Turaev invariant (Chern–Simons) *Invariant differential operator *Rozansky–Witten invariant *Vassiliev knot invariant *Dehn invariant *LMO invariant *Turaev–Viro invariant *Dijkgraaf–Witten invariant *Reshetikhin–Turaev invariant *Tau-invariant *I-Invariant *Klein J-invariant *Quantum isotopy invariant *Ermakov–Lewis invariant *Hermitian invariant *Goussarov–Habiro theory of finite-type invariant *Linear quantum invariant (orthogonal function invariant) *Murakami–Ohtsuki TQFT *Generalized Casson invariant *Casson-Walker invariant *Khovanov–Roza ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Knot Theory
In topology, knot theory is the study of knot (mathematics), mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are joined so it cannot be undone, the simplest knot being a ring (or "unknot"). In mathematical language, a knot is an embedding of a circle in 3-dimensional Euclidean space, \mathbb^3. Two mathematical knots are equivalent if one can be transformed into the other via a deformation of \mathbb^3 upon itself (known as an ambient isotopy); these transformations correspond to manipulations of a knotted string that do not involve cutting it or passing it through itself. Knots can be described in various ways. Using different description methods, there may be more than one description of the same knot. For example, a common method of describing a knot is a planar diagram called a knot diagram, in which any knot can be drawn in many different ways. Therefore, a fundamental p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
