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

  1. ^ 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.
  2. ^ Kontsevich, Maxim (1993). "Vassiliev's knot invariants". Adv. Soviet Math. 16: 137.
  3. ^ Watanabe, Tadayuki (2007). "Knotted trivalent graphs and construction of the LMO invariant from triangulations". Osaka J. Math. 44 (2): 351. Retrieved 4 December 2012.
  4. ^ Letzter, Gail (2004). "Invariant differential operators for quantum symmetric spaces, II". arXiv:math/0406194.
  5. ^ Sawon, Justin (2000). "Topological quantum field theory and hyperkähler geometry". arXiv:math/0009222.
  6. ^ Petit, Jerome (1999). "The invariant of Turaev-Viro from Group category" (PDF). hal.archives-ouvertes.fr. Retrieved 2019-11-04.
  7. ^ 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.


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