In the mathematical field of knot theory, a quantum knot invariant or quantum invariant of a knot or link is a linear sum of colored Jones polynomial of surgery presentations of the knot complement.
List of invariants Finite type invariant Kontsevich invariant Kashaev's invariant 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–Rozansky invariant HOMFLY polynomial K-theory invariants Atiyah–Patodi–Singer eta invariant Link invariant Casson invariant Seiberg–Witten invariants Gromov–Witten invariant Arf invariant Hopf invariant
See also Invariant theory Framed knot Chern–Simons theory Algebraic geometry Seifert surface Geometric invariant theory
References
Further reading
External links Quantum invariants of knots and 3-manifolds By Vladimir G. Turaev