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] [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 [8]
- 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
- ↑ Reshetikhin, N. & Turaev, V. (1991). "Invariants of 3-manifolds via link polynomials and quantum groups". Invent. Math. 103 (1): 547. doi:10.1007/BF01239527. Retrieved 4 December 2012.
- ↑ 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.
- ↑ [math/0406194] Invariant differential operators for quantum symmetric spaces, II
- ↑ [math/0009222v1] Topological quantum field theory and hyperk\"ahler geometry
- ↑ http://hal.archives-ouvertes.fr/docs/00/09/02/99/PDF/equality_arxiv_1.pdf
- ↑ http://knot.kaist.ac.kr/7thkgtf/Lawton1.pdf
- ↑ Invariants of 3-manifolds via link polynomials and quantum groups - Springer
Further reading
- Freedman, Michael H. (1990). Topology of 4-manifolds. Princeton, N.J: Princeton University Press. ISBN 0691085773.
- Ohtsuki, Tomotada (December 2001). Quantum Invariants. World Scientific Publishing Company. ISBN 9789810246754.