Quantum invariant
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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
[edit]- 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
[edit]- Invariant theory
- Framed knot
- Chern–Simons theory
- Algebraic geometry
- Seifert surface
- Geometric invariant theory
References
[edit]- ^ a b 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
[edit]- 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
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