Quantum Invariant for Torus Link and Modular Forms

Communications in Mathematical Physics

Volumn 246, Issue 2, 2004, Pages 403-426

  Hikami, Kazuhiro ^a  

^a UNIVERSITY OF TOKYO   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 2142806648     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-004-1046-2     Document Type: Article

References (21)

1. Andrews, G. E.: The Theory of Partitions. London: Addison-Wesley, 1976
2. Hikami, K.: Volume conjecture and asymptotic expansion of q-series. Exp. Math. (2003). to appear
3. Hikami, K.: q-series and L-functions related to half-derivatives of the Andrews-Gordon identity. Ramanujan J., (2003), to appear
4. Kac, V. G.: Infinite Dimensional Lie Algebras, Third ed. Cambridge: Cambridge Univ. Press, 1990
5. Kashaev, R. M.: A link invariant from quantum dilogarithm. Mod. Phys. Lett. A 10 1409-1418 (1995)
6. Kashaev, R. M.: The hyperbolic volume of knots from quantum dilogarithm. Lett. Math. Phys. 39, 269-275 (1997)
7. Kashaev, R. M., Tirkkonen, O.: Proof of the volume conjecture for torus knots. Zap. Nauch. Sem. POMI, 269, 262-268 (2000)
8. Lawrence, R., Rozansky, L.: Witten-Reshetikhin-Turaev invariants of Seifert manifolds. Commun. Math. Phys. 205, 287-314 (1999)
9. Lawrence, R., Zagier, D.: Modular forms and quantum invariants of 3-manifolds. Asian J. Math., 3, 93-107 (1999)
10. Lickerish, R.: An Introduction to Knot Theory. New York: Springer, 1997
11. Macdonald, I. G.: Affine root systems and Dedekind's η-function. Invent. Math. 15, 91-143 (1972)
12. Morton, H. R.: The coloured Jones function and Alexander polynomial for torus knots. Proc. Cambridge Philos. Soc. 117, 129-135 (1995)
13. Murakami, H.: Kashaev's invariant and the volume of a hyperbolic knot after Yokota. In: "Physics and Combinatorics", A. N. Kirillov, A. Tsuchiya, H. Umemura, eds., Singapore: World Scientific, 2001, pp. 244-272
14. Murakami, H., Murakami, J.: The colored Jones polynomials and the simplicial volume of a knot. Acta Math. 186, pp. 85-104 (2001)
15. Rosso, M., Jones, V.: On the invariants of torus knots derived from quantum groups. J. Knot Theory Ramifications 2, 97-112 (1993)
16. Rozansky, L.: Higher order terms in the Melvin-Morton expansion of the colored Jones polynomial. Commun. Math. Phys. 183, (1997)
17. Stoimenow, A.: Enumeration of chord diagrams and an upper bound forVassiliev invariants. J. Knot Theory Ramifications 7, 93-114 (1998)
18. Yokota, Y.: On the volume conjecture for hyperbolic knots. math.QA/0009165, (2000)
19. Zagier, D.: Vassiliev invariants and a strange identity related to the Dedekind eta-function. Topology 40, 945-960 (2001)
20. Zwegers, S. P.: Mock ν-functions and real analytic modular forms. In "q-Series with Applications to Combinatorics, Number Theory, and Physics", B. C. Berndt, K. Ono, eds., Providence, RI: Am. Math. Soc., 2001, pp. 269-277
21. Zwegers, S. P.: Mock Theta Functions. PhD thesis, Universiteit Utrecht, 2002