메뉴 건너뛰기




Volumn 15, Issue 8, 2006, Pages 983-1000

Is the Jones polynomial of a knot really a polynomial?

Author keywords

A polynomial; AJ Conjecture; Habiro ring; Holonomic functions; Homology spheres; Jones polynomial; Kauffman bracket; Knots; TQFT

Indexed keywords


EID: 33751101112     PISSN: 02182165     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218216506004919     Document Type: Conference Paper
Times cited : (4)

References (29)
  • 1
    • 33751084488 scopus 로고    scopus 로고
    • The Aarhus integral of rational homology 3-spheres III: The relation with the Le-Murakami-Ohtsuki invariant
    • D. Bar-Natan, S. Garoufalidis, L. Rozansky and D. Thurston, The Aarhus integral of rational homology 3-spheres III: The relation with the Le-Murakami-Ohtsuki invariant, Selecta Math. 10 (2004) 305-324.
    • (2004) Selecta Math. , vol.10 , pp. 305-324
    • Bar-Natan, D.1    Garoufalidis, S.2    Rozansky, L.3    Thurston, D.4
  • 3
    • 0002460142 scopus 로고
    • Modules over a ring of differential operators. An investigation of the fundamental solutions of equations with constant coefficients
    • English translation: 89-101
    • I. N. Bernstein, Modules over a ring of differential operators. An investigation of the fundamental solutions of equations with constant coefficients, Funct. Anal,. Appl. 5 (1971) 1-16; English translation: 89-101.
    • (1971) Funct. Anal,. Appl. , vol.5 , pp. 1-16
    • Bernstein, I.N.1
  • 4
    • 0001620260 scopus 로고
    • The analytic continuation of generalized functions with respect to a parameter
    • English translation: 273-285
    • I. N. Bernstein, The analytic continuation of generalized functions with respect to a parameter, Funct. Anal. Appl. 6 (1972) 26-40; English translation: 273-285.
    • (1972) Funct. Anal. Appl. , vol.6 , pp. 26-40
    • Bernstein, I.N.1
  • 5
    • 0002499459 scopus 로고
    • Démonstration "automatique" d'identités et fonctions hypergéométriques (d'aprés D. Zeilberger)
    • Astérisque, Exp. No. 746 41-91
    • P. Cartier, Démonstration "automatique" d'identités et fonctions hypergéométriques (d'aprés D. Zeilberger), Séminaire Bourbaki, Vol. 1991/92. Astérisque, No. 206 (1992), Exp. No. 746 41-91.
    • (1992) Séminaire Bourbaki , vol.1991 , Issue.92-206
    • Cartier, P.1
  • 6
    • 0002576110 scopus 로고
    • Plane curves associated to character varieties of 3-manifolds
    • D. Cooper, D. M. Culler, H. Gillet, D. Long and P. Shalen, Plane curves associated to character varieties of 3-manifolds, Invent. Math. 118 (1994) 47-84.
    • (1994) Invent. Math. , vol.118 , pp. 47-84
    • Cooper, D.1    Culler, D.M.2    Gillet, H.3    Long, D.4    Shalen, P.5
  • 7
    • 23744451374 scopus 로고    scopus 로고
    • The colored Jones function is q-holonomic
    • S. Garoufalidis and T. T. Q. Le, The colored Jones function is q-holonomic, Geom. Topol. 9 (2005) 1253-1293.
    • (2005) Geom. Topol. , vol.9 , pp. 1253-1293
    • Garoufalidis, S.1    Le, T.T.Q.2
  • 8
    • 17144362238 scopus 로고    scopus 로고
    • On the characteristic and deformation varieties of a knot
    • Geometry and Topology Monographs
    • S. Garoufalidis and T. T. Q. Le, On the characteristic and deformation varieties of a knot, in Proceedings of the CassonFest, Geometry and Topology Monographs, Vol. 7 (2004), pp. 291-309.
    • (2004) Proceedings of the CassonFest , vol.7 , pp. 291-309
    • Garoufalidis, S.1    Le, T.T.Q.2
  • 9
    • 11244283359 scopus 로고    scopus 로고
    • 2 invariants of knots and integral homology spheres
    • 2 invariants of knots and integral homology spheres, Geometry and Topology Monographs, Vol. 4 (2002), pp. 55-68.
    • (2002) Geometry and Topology Monographs , vol.4 , pp. 55-68
    • Habiro, K.1
  • 10
    • 18444405552 scopus 로고    scopus 로고
    • Cyclotomic completions of polynomial rings
    • K. Habiro, Cyclotomic completions of polynomial rings, Publ. Res. Inst. Math. Sci. 40 (2004) 1127-1146.
    • (2004) Publ. Res. Inst. Math. Sci. , vol.40 , pp. 1127-1146
    • Habiro, K.1
  • 12
    • 11244292505 scopus 로고    scopus 로고
    • Difference equation of the colored Jones polynomial for torus knot
    • K. Hikami, Difference equation of the colored Jones polynomial for torus knot, Int. J. Math. 15 (2004) 959-965.
    • (2004) Int. J. Math. , vol.15 , pp. 959-965
    • Hikami, K.1
  • 13
    • 0003936304 scopus 로고
    • Graduate Studies in Mathematics (American Mathematical Society)
    • J. C. Jantzen, Lecture on Quantum Groups, Graduate Studies in Mathematics, Vol. 6 (American Mathematical Society, 1995).
    • (1995) Lecture on Quantum Groups , vol.6
    • Jantzen, J.C.1
  • 14
    • 0001665177 scopus 로고
    • Hecke algebra, representation of braid groups and link polynomials
    • V. Jones, Hecke algebra, representation of braid groups and link polynomials, Ann. Math. 126 (1987) 335-388.
    • (1987) Ann. Math. , vol.126 , pp. 335-388
    • Jones, V.1
  • 15
    • 0000282829 scopus 로고
    • State models and the Jones polynomial
    • L. Kauffman, State models and the Jones polynomial, Topology 26 (1987) 395-407.
    • (1987) Topology , vol.26 , pp. 395-407
    • Kauffman, L.1
  • 16
    • 0001673424 scopus 로고
    • The 3-manifold invariants of Witten and Reshetikhin-Turaev for sl(2, C)
    • R. Kirby and P. Melvin, The 3-manifold invariants of Witten and Reshetikhin-Turaev for sl(2, C), Invent. Math. 105 (1991) 473-545.
    • (1991) Invent. Math. , vol.105 , pp. 473-545
    • Kirby, R.1    Melvin, P.2
  • 17
    • 21844518572 scopus 로고
    • The coloured Jones function
    • P. Melvin and H. Morton, The coloured Jones function, Commun. Math. Phys. 169 (1995) 501-520.
    • (1995) Commun. Math. Phys. , vol.169 , pp. 501-520
    • Melvin, P.1    Morton, H.2
  • 18
    • 0032067814 scopus 로고    scopus 로고
    • A universal quantum invariant of 3-manifolds
    • T. T. Q. Le, J. Murakami and T. Ohtsuki, A universal quantum invariant of 3-manifolds, Topology 37 (1998) 539-574.
    • (1998) Topology , vol.37 , pp. 539-574
    • Le, T.T.Q.1    Murakami, J.2    Ohtsuki, T.3
  • 19
    • 0034164757 scopus 로고    scopus 로고
    • Integrality and symmetry of quantum link invariants
    • T. T. Q. Le, J. Murakami and T. Ohtsuki, Integrality and symmetry of quantum link invariants, Duke Math. J. 102 (2000) 273-306.
    • (2000) Duke Math. J. , vol.102 , pp. 273-306
    • Le, T.T.Q.1    Murakami, J.2    Ohtsuki, T.3
  • 20
    • 33749065744 scopus 로고    scopus 로고
    • The colored Jones polynomial and the A-polynomial of knots
    • to appear in
    • T. T. Q. Le, J. Murakami and T. Ohtsuki, The colored Jones polynomial and the A-polynomial of knots, to appear in Adv. Math.
    • Adv. Math.
    • Le, T.T.Q.1    Murakami, J.2    Ohtsuki, T.3
  • 24
    • 0002203695 scopus 로고    scopus 로고
    • Skein algebra of a group
    • Banach Center Publications (Polish Academy of Sciences, Warsaw)
    • J. Przytycki and A. Sikora, Skein algebra of a group, Knot Theory, Banach Center Publications, Vol. 42 (Polish Academy of Sciences, Warsaw, 1998), pp. 297-306.
    • (1998) Knot Theory , vol.42 , pp. 297-306
    • Przytycki, J.1    Sikora, A.2
  • 25
    • 34249960869 scopus 로고
    • Ribbon graphs and their invariants derived from quantum groups
    • N. Reshetikhin and V. Turaev, Ribbon graphs and their invariants derived from quantum groups, Commun. Math. Phys. 127 (1990) 1-26.
    • (1990) Commun. Math. Phys. , vol.127 , pp. 1-26
    • Reshetikhin, N.1    Turaev, V.2
  • 26
    • 0010192627 scopus 로고
    • Systémes holonomes d'équations aux q-différences
    • Lisbon (de Gruyter, Berlin)
    • C. Sabbah, Systémes holonomes d'équations aux q-différences, in D-Modules and Microlocal Geometry, Lisbon (1990) (de Gruyter, Berlin, 1993), pp. 125-147.
    • (1990) D-modules and Microlocal Geometry , pp. 125-147
    • Sabbah, C.1
  • 27
    • 0003523790 scopus 로고
    • de Gruyter Studies in Mathematics (Walter de Gruyter &: Co., Berlin)
    • V. Turaev, Quantum Invariants of Knots and 3-Manifolds, de Gruyter Studies in Mathematics, Vol. 18 (Walter de Gruyter &: Co., Berlin, 1994).
    • (1994) Quantum Invariants of Knots and 3-Manifolds , vol.18
    • Turaev, V.1
  • 28
    • 0001601404 scopus 로고
    • A holonomic systems approach to special functions identities
    • D. Zeilberger, A holonomic systems approach to special functions identities, J. Comput. Appl. Math. 32 (1990) 321-368.
    • (1990) J. Comput. Appl. Math. , vol.32 , pp. 321-368
    • Zeilberger, D.1
  • 29
    • 0001195414 scopus 로고    scopus 로고
    • Vassiliev invariants and a strange identity related to the Dedekind eta-function
    • D. Zagier, Vassiliev invariants and a strange identity related to the Dedekind eta-function, Topology 40 (2001) 945-960.
    • (2001) Topology , vol.40 , pp. 945-960
    • Zagier, D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.