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Quantum invariant

November 27, 2023

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

See also edit

References edit

  1. ^ Reshetikhin, N. & Turaev, V. (1991). "Invariants of 3-manifolds via link polynomials and quantum groups". Invent. Math. 103 (1): 547. Bibcode:1991InMat.103..547R. doi:10.1007/BF01239527. S2CID 123376541.
  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. ^ "Data" (PDF). hal.archives-ouvertes.fr. 1999. Retrieved 2019-11-04.
  7. ^ (PDF). knot.kaist.ac.kr. Archived from the original (PDF) on 20 July 2007. Retrieved 13 January 2022.{{cite web}}: CS1 maint: archived copy as title (link)
  8. ^ "Invariants of 3-manifolds via link polynomials and quantum groups - Springer". doi:10.1007/BF01239527. S2CID 123376541. {{cite journal}}: Cite journal requires |journal= (help)

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 edit

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


 

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November 27, 2023
quantum, invariant, mathematical, field, knot, theory, quantum, knot, invariant, quantum, invariant, knot, link, linear, colored, jones, polynomial, surgery, presentations, knot, complement, contents, list, invariants, also, references, further, reading, exter. 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 Contents 1 List of invariants 2 See also 3 References 4 Further reading 5 External linksList of invariants editFinite 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 invariants Gromov Witten invariant Arf invariant Hopf invariantSee also editInvariant theory Framed knot Chern Simons theory Algebraic geometry Seifert surface Geometric invariant theoryReferences edit Reshetikhin N amp Turaev V 1991 Invariants of 3 manifolds via link polynomials and quantum groups Invent Math 103 1 547 Bibcode 1991InMat 103 547R doi 10 1007 BF01239527 S2CID 123376541 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 hyperkahler geometry arXiv math 0009222 Data PDF hal archives ouvertes fr 1999 Retrieved 2019 11 04 Archived copy PDF knot kaist ac kr Archived from the original PDF on 20 July 2007 Retrieved 13 January 2022 a href Template Cite web html title Template Cite web cite web a CS1 maint archived copy as title link Invariants of 3 manifolds via link polynomials and quantum groups Springer doi 10 1007 BF01239527 S2CID 123376541 a href Template Cite journal html title Template Cite journal cite journal a Cite journal requires journal help Further reading editFreedman 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 editQuantum invariants of knots and 3 manifolds By Vladimir G Turaev nbsp This knot theory related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Quantum invariant amp oldid 1095183563, wikipedia, wiki, book, books, library,

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