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Volumn 16, Issue 6, 2005, Pages 661-685

On the quantum invariant for the brieskorn homology spheres

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EID: 21644469654     PISSN: 0129167X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0129167X05003004     Document Type: Article
Times cited : (44)

References (44)
  • 3
    • 0010882054 scopus 로고
    • Infinite conformal symmetry in two-dimensional quantum field theory
    • A. A. Belavin, A. M. Polyakov and A. B. Zamolodchikov, Infinite conformal symmetry in two-dimensional quantum field theory, Nucl. Phys. B241 (1984) 333-380.
    • (1984) Nucl. Phys. , vol.B241 , pp. 333-380
    • Belavin, A.A.1    Polyakov, A.M.2    Zamolodchikov, A.B.3
  • 4
    • 84960552822 scopus 로고
    • Instanton homology of Seifert fibered homology three spheres
    • R. Fintushel and R. Stern, Instanton homology of Seifert fibered homology three spheres, Proc. London Math. Soc. 61 (1990) 109-137.
    • (1990) Proc. London Math. Soc. , vol.61 , pp. 109-137
    • Fintushel, R.1    Stern, R.2
  • 5
    • 0011401976 scopus 로고
    • Reidemeister torsion, spectral sequences, and Brieskorn spheres
    • D. S. Freed, Reidemeister torsion, spectral sequences, and Brieskorn spheres, J. Reine Angew. Math. 429 (1992) 75-89.
    • (1992) J. Reine Angew. Math. , vol.429 , pp. 75-89
    • Freed, D.S.1
  • 6
    • 0002059464 scopus 로고
    • Computer calculation of Witten's 3-manifold invariant
    • D. S. Freed and R. E. Gompf, Computer calculation of Witten's 3-manifold invariant, Commun. Math. Phys. 141 (1991) 79-117.
    • (1991) Commun. Math. Phys. , vol.141 , pp. 79-117
    • Freed, D.S.1    Gompf, R.E.2
  • 7
    • 0041075797 scopus 로고
    • Casson's invariant of Seifert homology 3-spheres
    • S. Fukuhara, Y. Matsumoto and K. Sakamoto, Casson's invariant of Seifert homology 3-spheres, Math. Ann. 287 (1990) 275-285.
    • (1990) Math. Ann. , vol.287 , pp. 275-285
    • Fukuhara, S.1    Matsumoto, Y.2    Sakamoto, K.3
  • 8
    • 11244292505 scopus 로고    scopus 로고
    • Difference equation of the colored Jones polynomial for the torus knot
    • K. Hikami, Difference equation of the colored Jones polynomial for the torus knot, Int. J. Math. 15 (2004) 959-965.
    • (2004) Int. J. Math. , vol.15 , pp. 959-965
    • Hikami, K.1
  • 9
    • 11244337993 scopus 로고    scopus 로고
    • Q-series and L-functions related to half-derivatives of the Andrews-Gordon identity
    • to appear in
    • _, q-series and L-functions related to half-derivatives of the Andrews-Gordon identity, to appear in Ramanujan J. (2004).
    • (2004) Ramanujan J.
  • 10
    • 2142806648 scopus 로고    scopus 로고
    • Quantum invariant for torus link and modular forms
    • _, Quantum invariant for torus link and modular forms, Commun. Math. Phys. 246 (2004) 403-426.
    • (2004) Commun. Math. Phys. , vol.246 , pp. 403-426
  • 11
    • 17144439538 scopus 로고    scopus 로고
    • Torus knot and minimal model
    • K. Hikami and A. N. Kirillov, Torus knot and minimal model, Phys. Lett. B575 (2003) 343-348.
    • (2003) Phys. Lett. , vol.B575 , pp. 343-348
    • Hikami, K.1    Kirillov, A.N.2
  • 13
    • 0000440716 scopus 로고
    • Chern-Simons-witten invariants of lens spaces and torus bundles, and the semiclassical approximation
    • L. C. Jeffrey, Chern-Simons-Witten invariants of lens spaces and torus bundles, and the semiclassical approximation, Commun. Math. Phys. 147 (1992) 563-604.
    • (1992) Commun. Math. Phys. , vol.147 , pp. 563-604
    • Jeffrey, L.C.1
  • 14
    • 84968518084 scopus 로고
    • A polynomial invariant for knots via von Neumann algebras
    • V. F. R. Jones, A polynomial invariant for knots via von Neumann algebras, Bull. Amer. Math. Soc. 12 (1985) 103-111.
    • (1985) Bull. Amer. Math. Soc. , vol.12 , pp. 103-111
    • Jones, V.F.R.1
  • 15
    • 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
  • 16
    • 0002124203 scopus 로고
    • Dedekind sums, μ-invariants and the signature cocycle
    • _, Dedekind sums, μ-invariants and the signature cocycle, Math. Ann. 299 (1994) 231-267.
    • (1994) Math. Ann. , vol.299 , pp. 231-267
  • 17
    • 0000669016 scopus 로고
    • Chern-Simons invariants of 3-manifolds and representation spaces of knot groups
    • P. A. Kirk and E. P. Klassen, Chern-Simons invariants of 3-manifolds and representation spaces of knot groups, Math. Ann. 287 (1990) 343-367.
    • (1990) Math. Ann. , vol.287 , pp. 343-367
    • Kirk, P.A.1    Klassen, E.P.2
  • 18
    • 0003911106 scopus 로고
    • Grundlehren der Mathematischen Wissenschaften Springer, Berlin
    • S. Lang, Introduction to Modular Forms, Grundlehren der Mathematischen Wissenschaften, Vol. 222 (Springer, Berlin, 1976).
    • (1976) Introduction to Modular Forms , vol.222
    • Lang, S.1
  • 19
    • 21844485337 scopus 로고
    • Asymptotic expansions of witten-reshetikhin-turaev invariants for some simple 3-manifolds
    • R. Lawrence, Asymptotic expansions of Witten-Reshetikhin-Turaev invariants for some simple 3-manifolds, J. Math. Phys. 36 (1995) 6106-6129.
    • (1995) J. Math. Phys. , vol.36 , pp. 6106-6129
    • Lawrence, R.1
  • 20
    • 0001284488 scopus 로고    scopus 로고
    • Witten-reshetikhin-turaev invariants of 3-manifolds as holomorphic functions
    • J. E. Andersen, J. Dupont, H. Pedersen and A. Swann, Lecture Notes in Pure and Applied Mathematics, Dekker, New York
    • _, Witten-Reshetikhin-Turaev invariants of 3-manifolds as holomorphic functions, in Geometry and Physics, eds. J. E. Andersen, J. Dupont, H. Pedersen and A. Swann, Lecture Notes in Pure and Applied Mathematics, Vol. 184 (Dekker, New York, 1996), pp. 363-377.
    • (1996) Geometry and Physics , vol.184 , pp. 363-377
  • 21
    • 0033480012 scopus 로고    scopus 로고
    • On Ohtsuki's invariants of homology 3-spheres
    • _, On Ohtsuki's invariants of homology 3-spheres, J. Knot Theory Ramification 8 (1999) 1049-1063.
    • (1999) J. Knot Theory Ramification , vol.8 , pp. 1049-1063
  • 22
    • 0033245033 scopus 로고    scopus 로고
    • Witten-Reshetikhin-Turaev invariants of Seifert manifolds
    • R. Lawrence and L. Rozansky, Witten-Reshetikhin-Turaev invariants of Seifert manifolds, Commun. Math. Phys. 205 (1999) 287-314.
    • (1999) Commun. Math. Phys. , vol.205 , pp. 287-314
    • Lawrence, R.1    Rozansky, L.2
  • 23
    • 0012848870 scopus 로고    scopus 로고
    • Modular forms and quantum invariants of 3-manifolds
    • R. Lawrence and D. Zagier, Modular forms and quantum invariants of 3-manifolds, Asian J. Math. 3 (1999) 93-107.
    • (1999) Asian J. Math. , vol.3 , pp. 93-107
    • Lawrence, R.1    Zagier, D.2
  • 24
    • 0038012561 scopus 로고    scopus 로고
    • Quantum invariants of 3-manifolds: Integrality, splitting, and perturbative expansion
    • T. T. Q. Le, Quantum invariants of 3-manifolds: Integrality, splitting, and perturbative expansion, Topology Appl. 127 (2003) 125-152.
    • (2003) Topology Appl. , vol.127 , pp. 125-152
    • Le, T.T.Q.1
  • 25
    • 0000269757 scopus 로고
    • On the 3-dimensional brieskorn manifolds M(p, q, r)
    • L. P. Neuwirth, Papers Dedicated to the Memory of R. H. Fox. Princeton University Press
    • J. Milnor, On the 3-dimensional Brieskorn manifolds M(p, q, r), in Knots, Groups, and 3-Manifolds, ed. L. P. Neuwirth, Papers Dedicated to the Memory of R. H. Fox. (Princeton University Press, 1975), pp. 175-225.
    • (1975) Knots, Groups, and 3-Manifolds , pp. 175-225
    • Milnor, J.1
  • 26
    • 0001822390 scopus 로고
    • Lattice points in a tetrahedron and generalized Dedekind sums
    • L. J. Mordell, Lattice points in a tetrahedron and generalized Dedekind sums, J. Indian Math. Soc. (NS) 15 (1951) 41-46.
    • (1951) J. Indian Math. Soc. (NS) , vol.15 , pp. 41-46
    • Mordell, L.J.1
  • 27
    • 84973963366 scopus 로고
    • Quantum SU(2)-invariants dominate Casson's SU(2)-invariant
    • H. Murakami, Quantum SU(2)-invariants dominate Casson's SU(2)-invariant, Math. Proc. Cambridge Philos. Soc. 115 (1993) 253-281.
    • (1993) Math. Proc. Cambridge Philos. Soc. , vol.115 , pp. 253-281
    • Murakami, H.1
  • 28
    • 84973985319 scopus 로고
    • Quantum SO(3) invariants dominate the SU(2) invariant of Casson and Walker
    • _, Quantum SO(3) invariants dominate the SU(2) invariant of Casson and Walker, Math. Proc. Cambridge Philos. Soc. 117 (1995) 237-249.
    • (1995) Math. Proc. Cambridge Philos. Soc. , vol.117 , pp. 237-249
  • 29
    • 84974220831 scopus 로고
    • A polynomial invariant of integral homology 3-spheres
    • T. Ohtsuki, A polynomial invariant of integral homology 3-spheres, Math. Proc. Cambridge Philos. Soc. 117 (1995) 83-112.
    • (1995) Math. Proc. Cambridge Philos. Soc. , vol.117 , pp. 83-112
    • Ohtsuki, T.1
  • 30
    • 0030546896 scopus 로고    scopus 로고
    • A polynomial invariant of rational homology 3 spheres
    • _, A polynomial invariant of rational homology 3 spheres, Invent. Math. 123 (1996) 241-257.
    • (1996) Invent. Math. , vol.123 , pp. 241-257
  • 31
    • 0003805246 scopus 로고
    • Grundlehren der Mathematischen Wissenschaften, Springer, New York
    • H. Rademacher, Topics in Analytic Number Theory, Grundlehren der Mathematischen Wissenschaften, Vol. 169 (Springer, New York, 1973).
    • (1973) Topics in Analytic Number Theory , vol.169
    • Rademacher, H.1
  • 32
    • 0003874349 scopus 로고
    • Carus Mathematical Monographs, No. 16 Mathematical Association of America, Washington DC
    • H. Rademacher and E. Grosswald, Dedekind Sums, Carus Mathematical Monographs, No. 16 (Mathematical Association of America, Washington DC, 1972).
    • (1972) Dedekind Sums
    • Rademacher, H.1    Grosswald, E.2
  • 33
    • 0542373499 scopus 로고
    • Invariants of 3-manifolds via link polynomials and quantum groups
    • N. Yu. Reshetikhin and V. G. Turaev, Invariants of 3-manifolds via link polynomials and quantum groups, Invent. Math. 103 (1991) 547-597.
    • (1991) Invent. Math. , vol.103 , pp. 547-597
    • Reshetikhin, N.Yu.1    Turaev, V.G.2
  • 34
    • 21844507036 scopus 로고
    • A large k asymptotics of witten's invariant of seifert manifolds
    • L. Rozansky, A large k asymptotics of Witten's invariant of Seifert manifolds, Commun. Math. Phys. 171 (1995) 279-322.
    • (1995) Commun. Math. Phys. , vol.171 , pp. 279-322
    • Rozansky, L.1
  • 35
    • 0030545491 scopus 로고    scopus 로고
    • A contribution of the trivial connection to Jones polynomial and Witten's invariant of 3d manifolds I
    • _, A contribution of the trivial connection to Jones polynomial and Witten's invariant of 3d manifolds I, Commun. Math. Phys. 175 (1996) 275-296.
    • (1996) Commun. Math. Phys. , vol.175 , pp. 275-296
  • 36
    • 0030548964 scopus 로고    scopus 로고
    • A contribution of the trivial connection to Jones polynomial and Witten's invariant of 3d manifolds II
    • _, A contribution of the trivial connection to Jones polynomial and Witten's invariant of 3d manifolds II, Commun. Math. Phys. 175 (1996) 297-318.
    • (1996) Commun. Math. Phys. , vol.175 , pp. 297-318
  • 37
    • 0030530947 scopus 로고    scopus 로고
    • Residue formulas for the large k asymptotics of witten's invariants of seifert manifolds: The case of SU(2)
    • _, Residue formulas for the large k asymptotics of Witten's invariants of Seifert manifolds: The case of SU(2), Commun. Math. Phys. 178 (1996) 27-60.
    • (1996) Commun. Math. Phys. , vol.178 , pp. 27-60
  • 38
    • 0030486493 scopus 로고    scopus 로고
    • Witten's invariants of rational homology spheres at prime values of K and trivial connection contribution
    • _, Witten's invariants of rational homology spheres at prime values of K and trivial connection contribution, Commun. Math. Phys. 180 (1996) 297-324.
    • (1996) Commun. Math. Phys. , vol.180 , pp. 297-324
  • 39
    • 0031541571 scopus 로고    scopus 로고
    • The trivial connection contribution to witten's invariant and finite type invariants of rational homology spheres
    • _, The trivial connection contribution to Witten's invariant and finite type invariants of rational homology spheres, Commun. Math. Phys. 183 (1997) 23-54.
    • (1997) Commun. Math. Phys. , vol.183 , pp. 23-54
  • 40
    • 0031524343 scopus 로고    scopus 로고
    • Casson-Walker invariant of Seifert fibered rational homology spheres as quantum SO(3)-invariant
    • C. Sato, Casson-Walker invariant of Seifert fibered rational homology spheres as quantum SO(3)-invariant, J. Knot Theory Ramification 6 (1997) 79-93.
    • (1997) J. Knot Theory Ramification , vol.6 , pp. 79-93
    • Sato, C.1
  • 42
    • 0003763027 scopus 로고
    • Annals of Mathematics Studies Princeton University Press, Princeton
    • K. Walker, An Extension of Casson's Invariant, Annals of Mathematics Studies, Vol. 126 (Princeton University Press, Princeton, 1992).
    • (1992) An Extension of Casson's Invariant , vol.126
    • Walker, K.1
  • 43
    • 14644388676 scopus 로고
    • Quantum field theory and Jones' polynomial
    • E. Witten, Quantum field theory and Jones' polynomial, Commun. Math. Phys. 121 (1989) 351-399.
    • (1989) Commun. Math. Phys. , vol.121 , pp. 351-399
    • Witten, E.1
  • 44
    • 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


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