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Quantum invariant

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Quantum invariant

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

References

^ ^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 $\operatorname {SL} (2,\mathbb {C} )$ -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

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

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