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