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List of invariants

• Finite type invariant
• Kontsevich invariant
• Kashaev's invariant
• Witten–Reshetikhin–Turaev invariant (Chern–Simons)
• Invariant differential operator⁴
• Rozansky–Witten invariant
• Vassiliev knot invariant
• Dehn invariant
• LMO invariant⁵
• Turaev–Viro invariant
• Dijkgraaf–Witten invariant⁶
• Reshetikhin–Turaev invariant
• Tau-invariant
• I-Invariant
• Klein J-invariant
• Quantum isotopy invariant⁷
• 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 invariant⁸
• 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

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

References

1. 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. /wiki/Doi_(identifier) ↩

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. http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdf_1&handle=euclid.ojm/1183667985 ↩

4. Letzter, Gail (2004). "Invariant differential operators for quantum symmetric spaces, II". arXiv:math/0406194. /wiki/Gail_Letzter ↩

5. Sawon, Justin (2000). "Topological quantum field theory and hyperkähler geometry". arXiv:math/0009222. /wiki/ArXiv_(identifier) ↩

6. Petit, Jerome (1999). "The invariant of Turaev-Viro from Group category" (PDF). hal.archives-ouvertes.fr. Retrieved 2019-11-04. http://hal.archives-ouvertes.fr/docs/00/09/02/99/PDF/equality_arxiv_1.pdf ↩

7. Lawton, Sean (June 28, 2007). "Generators of SL ⁡ ( 2 , C ) {\displaystyle \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. https://web.archive.org/web/20070720181358/http://knot.kaist.ac.kr/7thkgtf/Lawton1.pdf ↩

8. 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. /wiki/Doi_(identifier) ↩