Quantum invariant

In the mathematical field of knot theory, a quantum invariant of a knot or link is a linear sum of colored Jones polynomial of surgery presentations of the knot complement.^[1]

List of invariants

• Finite type invariant
• Kontsevich invariant
• Kashaev's invariant
• Witten–Reshetikhin–Turaev invariant (Chern–Simons)
• Invariant differential operator^[2]
• Rozansky–Witten invariant
• Vassiliev knot invariant
• Dehn invariant
• LMO invariant ^[3]
• Turaev–Viro invariant
• Dijkgraaf–Witten invariant ^[4]
• Reshetikhin–Turaev invariant
• Tau-invariant
• I-Invariant
• Klein J-invariant
• Quantum isotopy invariant ^[5]
• 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 quantum invariant^[6]
• K-theory invariants
• Atiyah–Patodi–Singer eta invariant
• Link invariant ^[7]
• Casson invariant
• Seiberg–Witten invariant
• 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

• Reference to Frank Quinn: Freedman, Michael H.; Quinn, Frank (1990). Topology of 4-Manifolds. Princeton: Princeton University Press. ISBN 0691085773. 
• Reshetikhin, N. & Turaev, V. (1991). "Invariants of 3-manifolds via link polynomials and quantum groups". Invent. Math. 103 (1): 547–597. doi:10.1007/BF01239527. 
• Kontsevich, Maxim (1993). "Vassiliev's knot invariants". Adv. Soviet Math. 16: 137–150. 
• Ohtsuki, Tomotada (2002). Quantum Invariants: A Study of Knots, 3-Manifolds, and their Sets. Series on Knots and Everything. 29. Singapore: World Scientific Publishing. ISBN 9810246757. 

External links

• Quantum invariants of knots and 3-manifolds By Vladimir G. Turaev