This is a preview of subscription content, log in via an institution to check access.
References
Akutsu, Y., Deguchi, T., &Ohtsuki, T., Invariants of colored links.,J. Knot. Theory Ramifications, 1 (1992), 161–184.
Bar-Natan, D. &Garoufalidis, S., On the Melvin-Morton-Rozansky conjecture.Invent. Math., 125 (1996), 103–133.
Burau, W., Kennzeichnung der Schlauchknoten.Abh. Math. Sem. Univ. Hambrug, 9 (1932), 125–133.
Burde, G., &Zieschang, H.,Knots de Gruyter Stud. Math., 5, de Gruyter, Berlin, 1985
Deguchi, T., On the new hierarchy of the colored braid matrices.J. Phys. Soc. Japan, 60 (1991), 3978–3979.
—, Miltivariable invariants of colored links generalizing the Alexander polynomial, inProceedings of the Conference on Quantum Topology (Manhattan, KS, 1993), pp. 67–85. World Sci. Publishing, River Edge, NJ, 1994.
Drinfel'd, V. G., Quantum groups, inProceedings of the International Congress of Mathematicians, Vols., 1, 2 (Berkeley, CA, 1986) pp. 798–820. Amer. Math. Soc., Providence, RI, 1987.
Gordon, C. McA., Dehn surgery and satellite knots.,Trans. Amer. Math. Soc., 275 (1983), 687–708.
Gradshteyn, I. S. &Ryzhik, I. M.,Table of Integrals, Series, and Products. Corrected and enlarged edition edited by Alan. Jeffrey. Incorporating the 4th edition edited by Yu. V. Geronimus and M. Yu. Tseytlin. Translated from the Russian. Academic Press, New York, 1980.
Gromov, M., Volume and bounded cohomology.Inst. Hautes Études Sci. Publ. Math., 56 (1982), 5–99.
Jaco, W. H. &Shalen, P. B.,Seifert Fibered Spaces in 3-manifolds. Mem. Amer. Math. Soc., 21 (220), Amer. Math. Soc., Providence, RI, 1979.
Johannson, K.,Homotopy Equivalences of 3-manifolds with Boundaries. Lecture Notes in Math., 761. Springer-Verlag, Berlin, 1979.
Kashaev, R. M., A link invariant from quantum dilogarithm.Modern, Phys. Lett. A., 10 (1995), 1409–1418.
—, The hyperbolic volume of knots from the quantum dilogarithm.Lett. Math. Phys., 39 (1997), 269–275.
Kashaev, R. M. & Tirkkonen, O., Proof of the volume conjecture for torus knots.math. GT/9912210.
Kassel, C.,Quantum Groups. Graduate Texts in Math., 155. Springer-Verlag, New York, 1995.
Kirby, R., Problems in low-dimensional topology, inGeometric Topology (Athens, GA, 1993), pp. 35–473. Amer. Math. Soc., Providence, RI, 1997.
Kirby, R. &Melvin, P., The 3-manifold invariants of Witten and Reshetikhin-Turaev for sl (2,C).Invent. Math., 105 (1991), 473–545.
Melvin, P. M. &Morton, H. R., The coloured Jones function.Comm. Math. Phys., 169 (1995), 501–520.
Morton, H. R., The coloured Jones function and Alexander polynomial for torus knots.Math. Proc. Cambridge Philos. Soc., 117 (1995), 129–135.
Murakami, J., The parallel version of polynomial invariants of links.Osaka J. Math., 26 (1989), 1–55.
—, A state model for the multivariable Alexander polynomial.Pacific J. Math., 157 (1993), 109–135.
Rosso, M. &Jones, V., On the invariants of torus knots derived from quantum groups.J. Knot Theory Ramifications, 2 (1993), 97–112.
Rozansky, L., A contribution of the trivial connection to the Jones polynomial and Witten's invariant of 3d manifolds, I; II.Comm. Math. Phys., 175 (1996). 275–296; 297–318.
Ruberman, D., Mutation and volumes of knots inS 3.Invent. Math., 90 (1987), 189–215.
Soma, T., The Gromov invariant of links.Invent. Math., 64 (1981), 445–454.
Turaev, V. G., The Yang-Baxter equation and invariants of links.Invent. Math., 92 (1988), 527–553.
Vassiliev, V. A., Cohomology of knot spaces, inTheory of Singularities and Its Applications, pp. 23–69. Adv. Soviet Math., 1. Amer. Math. Soc., Providence, RI, 1990.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Murakami, H., Murakami, J. The colored Jones polynomials and the simplicial volume of a knot. Acta Math. 186, 85–104 (2001). https://doi.org/10.1007/BF02392716
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02392716