Quantum invariant

<h2 id="list-of-invariants">List of invariants</h2>
<ul><li><a href="/facts/Finite_type_invariant/s7qH76E8">Finite type invariant</a></li>
<li><a href="/facts/Kontsevich_invariant/am4zku9Q">Kontsevich invariant</a></li>
<li><a href="/facts/Volume_conjecture/1yhMHQF4">Kashaev's invariant</a></li>
<li><a href="/facts/Chern%25E2%2580%2593Simons_theory/AQ3Kayn3">Witten–Reshetikhin–Turaev invariant</a> (<a href="/facts/Chern%25E2%2580%2593Simons/AQ3Kayn3">Chern–Simons</a>)</li>
<li><a href="/facts/Invariant_differential_operator/yoFWKPV6">Invariant differential operator</a><a class="footnote-ref" id="fnref:4" href="#fn:4"><sup>4</sup></a></li>
<li>Rozansky–Witten invariant</li>
<li><a href="/facts/Vassiliev_knot_invariant/s7qH76E8">Vassiliev knot invariant</a></li>
<li><a href="/facts/Dehn_invariant/eahMFAAb">Dehn invariant</a></li>
<li>LMO invariant<a class="footnote-ref" id="fnref:5" href="#fn:5"><sup>5</sup></a></li>
<li>Turaev–Viro invariant</li>
<li>Dijkgraaf–Witten invariant<a class="footnote-ref" id="fnref:6" href="#fn:6"><sup>6</sup></a></li>
<li><a href="/facts/Reshetikhin%25E2%2580%2593Turaev_invariant/xQhD411L">Reshetikhin–Turaev invariant</a></li>
<li>Tau-invariant</li>
<li>I-Invariant</li>
<li><a href="/facts/Klein_J-invariant/H1a38AJF">Klein J-invariant</a></li>
<li>Quantum isotopy invariant<a class="footnote-ref" id="fnref:7" href="#fn:7"><sup>7</sup></a></li>
<li><a href="/facts/Ermakov%25E2%2580%2593Lewis_invariant/KvHmv43I">Ermakov–Lewis invariant</a></li>
<li>Hermitian invariant</li>
<li>Goussarov–Habiro theory of finite-type invariant</li>
<li>Linear quantum invariant (orthogonal function invariant)</li>
<li>Murakami–Ohtsuki <a href="/facts/TQFT/zHjrp3b8">TQFT</a></li>
<li><a href="/facts/Generalized_Casson_invariant/uRs2DNPp">Generalized Casson invariant</a></li>
<li><a href="/facts/Casson-Walker_invariant/uRs2DNPp">Casson-Walker invariant</a></li>
<li>Khovanov–Rozansky invariant</li>
<li><a href="/facts/HOMFLY_polynomial/0n0mc1Be">HOMFLY polynomial</a></li>
<li>K-theory invariants</li>
<li><a href="/facts/Atiyah%25E2%2580%2593Patodi%25E2%2580%2593Singer_eta_invariant/GH8vztLa">Atiyah–Patodi–Singer eta invariant</a></li>
<li><a href="/facts/Knot_invariant/BEvEEpHQ">Link invariant</a><a class="footnote-ref" id="fnref:8" href="#fn:8"><sup>8</sup></a></li>
<li><a href="/facts/Casson_invariant/uRs2DNPp">Casson invariant</a></li>
<li><a href="/facts/Seiberg%25E2%2580%2593Witten_invariants/VEKsxUBA">Seiberg–Witten invariants</a></li>
<li><a href="/facts/Gromov%25E2%2580%2593Witten_invariant/EJwrClYB">Gromov–Witten invariant</a></li>
<li><a href="/facts/Arf_invariant_(knot)/Ruh4VmJn">Arf invariant</a></li>
<li><a href="/facts/Hopf_invariant/6MCJDeDC">Hopf invariant</a></li></ul>
<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Invariant_theory/5fIUh9h3">Invariant theory</a></li>
<li><a href="/facts/Framed_knot/UMtKJ36m">Framed knot</a></li>
<li><a href="/facts/Chern%25E2%2580%2593Simons_theory/AQ3Kayn3">Chern–Simons theory</a></li>
<li><a href="/facts/Algebraic_geometry/rh7RHVp3">Algebraic geometry</a></li>
<li><a href="/facts/Seifert_surface/LqkqdPl8">Seifert surface</a></li>
<li><a href="/facts/Geometric_invariant_theory/l4eV0RdG">Geometric invariant theory</a></li></ul>

<h2 id="further-reading">Further reading</h2>
<ul><li>Freedman, Michael H. (1990). <a href="https://archive.org/details/topologyof4manif0000free"><i>Topology of 4-manifolds</i></a>. Princeton, N.J: Princeton University Press. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0691085777. <a href="/facts/OL_(identifier)/A13NLNNh">OL</a> <a href="https://openlibrary.org/books/OL2220094M">2220094M</a>.</li>
<li>Ohtsuki, Tomotada (December 2001). <i>Quantum Invariants</i>. World Scientific Publishing Company. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 9789810246754. <a href="/facts/OL_(identifier)/A13NLNNh">OL</a> <a href="https://openlibrary.org/books/OL9195378M">9195378M</a>.</li></ul>
<h2 id="external-links">External links</h2>
<ul><li><a href="https://books.google.com/books?id=yQRDNCJ0iOUC">Quantum invariants of knots and 3-manifolds By Vladimir G. Turaev</a></li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>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. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>Kontsevich, Maxim (1993). "Vassiliev's knot invariants". Adv. Soviet Math. 16: 137. <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
<li id="fn:3"><p>Watanabe, Tadayuki (2007). "Knotted trivalent graphs and construction of the LMO invariant from triangulations". Osaka J. Math. 44 (2): 351. Retrieved 4 December 2012. <a href="http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdf_1&handle=euclid.ojm/1183667985" target="_blank">http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdf_1&handle=euclid.ojm/1183667985</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li>
<li id="fn:4"><p>Letzter, Gail (2004). "Invariant differential operators for quantum symmetric spaces, II". arXiv:math/0406194. <a href="/wiki/Gail_Letzter" target="_blank">/wiki/Gail_Letzter</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li>
<li id="fn:5"><p>Sawon, Justin (2000). "Topological quantum field theory and hyperkähler geometry". arXiv:math/0009222. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li>
<li id="fn:6"><p>Petit, Jerome (1999). "The invariant of Turaev-Viro from Group category" (PDF). hal.archives-ouvertes.fr. Retrieved 2019-11-04. <a href="http://hal.archives-ouvertes.fr/docs/00/09/02/99/PDF/equality_arxiv_1.pdf" target="_blank">http://hal.archives-ouvertes.fr/docs/00/09/02/99/PDF/equality_arxiv_1.pdf</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li>
<li id="fn:7"><p>Lawton, Sean (June 28, 2007). "Generators of 
  
    
      
        SL
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        (
        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. <a href="https://web.archive.org/web/20070720181358/http://knot.kaist.ac.kr/7thkgtf/Lawton1.pdf" target="_blank">https://web.archive.org/web/20070720181358/http://knot.kaist.ac.kr/7thkgtf/Lawton1.pdf</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></p></li>
<li id="fn:8"><p>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. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></p></li>
</ol>

Quantum invariant open-in-new

Quantum invariant