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.[1][2][3]
List of invariants
- Finite type invariant
- Kontsevich invariant
- Kashaev’s invariant
- Witten–Reshetikhin–Turaev invariant (Chern–Simons)
- Invariant differential operator[4]
- Rozansky–Witten invariant
- Vassiliev knot invariant
- Dehn invariant
- LMO invariant[5]
- Turaev–Viro invariant
- Dijkgraaf–Witten invariant[6]
- Reshetikhin–Turaev invariant
- Tau-invariant
- I-Invariant
- Klein J-invariant
- Quantum isotopy invariant[7]
- 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[1]
- 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
- 1 2 Reshetikhin, N.; Turaev, V. G. (1991). “Invariants of 3-manifolds via link polynomials and quantum groups”. Inventiones Mathematicae. 103 (3): 547–597. doi:10.1007/BF01239527. MR 1091619.
- ↑
Kontsevich, Maxim (1993). “Vassiliev’s knot invariants”. Adv. Soviet Math. 16: 137. - ↑
Watanabe, Tadayuki (2007). “Knotted trivalent graphs and construction of the LMO invariant from triangulations”. Osaka J. Math. 44 (2): 351. Retrieved 4 December 2012. - ↑ Letzter, Gail (2004). “Invariant differential operators for quantum symmetric spaces, II”. arXiv:math/0406194.
- ↑ Sawon, Justin (2000). “Topological quantum field theory and hyperkähler geometry”. arXiv:math/0009222.
- ↑ Petit, Jerome (1999). “The invariant of Turaev-Viro from Group category” (PDF). hal.archives-ouvertes.fr. Retrieved 2019-11-04.
- ↑ Lawton, Sean (June 28, 2007). “Generators of
-Character Varieties of Arbitrary Rank Free Groups” (PDF). The 7th KAIST Geometric Topology Fair. Archived from the original (PDF) on 20 July 2007. Retrieved 13 January 2022.
Further reading
- Freedman, Michael H. (1990). Topology of 4-manifolds. Princeton, N.J: Princeton University Press. ISBN 978-0691085777. OL 2220094M.
- Ohtsuki, Tomotada (December 2001). Quantum Invariants. World Scientific Publishing Company. ISBN 9789810246754. OL 9195378M.
External links
This article is adapted from “Quantum invariant” on Wikipedia, written by its contributors, and used under CC BY-SA 4.0. Text on this page is available under the same licence. Source snapshot: Wikipedia via Kiwix, 2026-07-20.