메뉴 건너뛰기




Volumn , Issue 3, 2005, Pages 121-154

Quantum invariant, modular form, and lattice points

Author keywords

[No Author keywords available]

Indexed keywords


EID: 16244423041     PISSN: 10737928     EISSN: None     Source Type: Journal    
DOI: 10.1155/imrn.2005.121     Document Type: Article
Times cited : (33)

References (33)
  • 2
    • 0001502193 scopus 로고
    • New invariants of 3- And 4-dimensional manifolds
    • The Mathematical Heritage of Hermann Weyl (Durham, NC, 1987) (R. O. Wells Jr., ed.), American Mathematical Society, Rhode Island
    • M. Atiyah, New invariants of 3- and 4-dimensional manifolds, The Mathematical Heritage of Hermann Weyl (Durham, NC, 1987) (R. O. Wells Jr., ed.), Proc. Sympos. Pure Math., vol. 48, American Mathematical Society, Rhode Island, 1988, pp. 285-299.
    • (1988) Proc. Sympos. Pure Math. , vol.48 , pp. 285-299
    • Atiyah, M.1
  • 4
    • 84960552822 scopus 로고
    • Instanton homology of Seifert fibred homology three spheres
    • R. Fintushel and R. J. Stern, Instanton homology of Seifert fibred homology three spheres, Proc. London Math. Soc. (3) 61 (1990), no. 1, 109-137.
    • (1990) Proc. London Math. Soc. (3) , vol.61 , Issue.1 , pp. 109-137
    • Fintushel, R.1    Stern, R.J.2
  • 5
    • 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, Comm. Math. Phys. 141 (1991), no. 1, 79-117.
    • (1991) Comm. Math. Phys. , vol.141 , Issue.1 , pp. 79-117
    • Freed, D.S.1    Gompf, R.E.2
  • 6
    • 0041075797 scopus 로고
    • Casson's invariant of Seifen homology 3-spheres
    • S. Fukuhara, Y. Matsumoto, and K. Sakamoto, Casson's invariant of Seifen homology 3-spheres, Math. Ann. 287 (1990), no. 2, 275-285.
    • (1990) Math. Ann. , vol.287 , Issue.2 , pp. 275-285
    • Fukuhara, S.1    Matsumoto, Y.2    Sakamoto, K.3
  • 7
    • 1642365774 scopus 로고    scopus 로고
    • Volume conjecture and asymptotic expansion of q-series
    • K. Hikami, Volume conjecture and asymptotic expansion of q-series, Experiment. Math. 12 (2003), no. 3, 319-337.
    • (2003) Experiment. Math. , vol.12 , Issue.3 , pp. 319-337
    • Hikami, K.1
  • 8
    • 2142806648 scopus 로고    scopus 로고
    • Quantum invariant for torus link and modular forms
    • _, Quantum invariant for torus link and modular forms, Comm. Math. Phys. 246 (2004), no. 2, 403-426.
    • (2004) Comm. Math. Phys. , vol.246 , Issue.2 , 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. B 575 (2003), no. 3-4, 343-348.
    • (2003) Phys. Lett. B , vol.575 , Issue.3-4 , pp. 343-348
    • Hikami, K.1    Kirillov, A.N.2
  • 12
    • 0000440716 scopus 로고
    • Chern-Simons-Witten invariants of lens spaces and torus bundles, and the semi-classical approximation
    • L. C. Jeffrey, Chern-Simons-Witten invariants of lens spaces and torus bundles, and the semi-classical approximation, Comm. Math. Phys. 147 (1992), no. 3, 563-604.
    • (1992) Comm. Math. Phys. , vol.147 , Issue.3 , pp. 563-604
    • Jeffrey, L.C.1
  • 14
    • 0002045530 scopus 로고
    • Representation spaces of Seifert fibered homology spheres
    • P. A. Kirk and E. P. Klassen, Representation spaces of Seifert fibered homology spheres, Topology 30 (1991), no. 1, 77-95.
    • (1991) Topology , vol.30 , Issue.1 , pp. 77-95
    • Kirk, P.A.1    Klassen, E.P.2
  • 15
    • 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), no. 11, 6106-6129.
    • (1995) J. Math. Phys. , vol.36 , Issue.11 , pp. 6106-6129
    • Lawrence, R.1
  • 16
    • 0033480012 scopus 로고    scopus 로고
    • On Ohtsuki's invariants of homology 3-spheres
    • _, On Ohtsuki's invariants of homology 3-spheres, J. Knot Theory Ramifications 8 (1999), no. 8, 1049-1063.
    • (1999) J. Knot Theory Ramifications , vol.8 , Issue.8 , pp. 1049-1063
  • 17
    • 0033245033 scopus 로고    scopus 로고
    • Witten-Reshetikhin-Turaev invariants of Seifert manifolds
    • R. Lawrence and L. Rozansky, Witten-Reshetikhin-Turaev invariants of Seifert manifolds, Comm. Math. Phys. 205 (1999), no. 2, 287-314.
    • (1999) Comm. Math. Phys. , vol.205 , Issue.2 , pp. 287-314
    • Lawrence, R.1    Rozansky, L.2
  • 18
    • 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), no. 1, 93-107.
    • (1999) Asian J. Math. , vol.3 , Issue.1 , pp. 93-107
    • Lawrence, R.1    Zagier, D.2
  • 19
    • 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. (N.S.) 15 (1951), 41-46.
    • (1951) J. Indian Math. Soc. (N.S.) , vol.15 , pp. 41-46
    • Mordell, L.J.1
  • 20
    • 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 (1994), no. 2, 253-281.
    • (1994) Math. Proc. Cambridge Philos. Soc. , vol.115 , Issue.2 , pp. 253-281
    • Murakami, H.1
  • 21
    • 51249175292 scopus 로고
    • Casson invariant of links of singularities
    • W. Neumann and J. Wahl, Casson invariant of links of singularities, Comment. Math. Helv. 65 (1990), no. 1, 58-78.
    • (1990) Comment. Math. Helv. , vol.65 , Issue.1 , pp. 58-78
    • Neumann, W.1    Wahl, J.2
  • 22
    • 0030546896 scopus 로고    scopus 로고
    • A polynomial invariant of rational homology 3-spheres
    • T. Ohtsuki, A polynomial invariant of rational homology 3-spheres, Invent. Math. 123 (1996), no. 2, 241-257.
    • (1996) Invent. Math. , vol.123 , Issue.2 , pp. 241-257
    • Ohtsuki, T.1
  • 23
    • 0003227956 scopus 로고
    • Dedekind sums
    • The Mathematical Association of America, Washington, D.C
    • H. Rademacher and E. Grosswald, Dedekind Sums, The Carus Mathematical Monographs, no. 16, The Mathematical Association of America, Washington, D.C., 1972.
    • (1972) The Carus Mathematical Monographs , Issue.16
    • Rademacher, H.1    Grosswald, E.2
  • 24
    • 0542373499 scopus 로고
    • Invariants of 3-manifolds via link polynomials and quantum groups
    • N. Reshetikhin and V. G. Turaev, Invariants of 3-manifolds via link polynomials and quantum groups, Invent. Math. 103 (1991), no. 3, 547-597.
    • (1991) Invent. Math. , vol.103 , Issue.3 , pp. 547-597
    • Reshetikhin, N.1    Turaev, V.G.2
  • 25
    • 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, Comm. Math. Phys. 171 (1995), no. 2, 279-322.
    • (1995) Comm. Math. Phys. , vol.171 , Issue.2 , pp. 279-322
    • Rozansky, L.1
  • 26
    • 0030545491 scopus 로고    scopus 로고
    • A contribution of the trivial connection to the Jones polynomial and Witten's invariant of 3d manifolds. I
    • _, A contribution of the trivial connection to the Jones polynomial and Witten's invariant of 3d manifolds. I, Comm. Math. Phys. 175 (1996), no. 2, 275-296.
    • (1996) Comm. Math. Phys. , vol.175 , Issue.2 , pp. 275-296
  • 27
    • 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), Comm. Math. Phys. 178 (1996), no. 1, 27-60.
    • (1996) Comm. Math. Phys. , vol.178 , Issue.1 , pp. 27-60
  • 28
    • 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, Comm. Math. Phys. 183 (1997), no. 1, 23-54.
    • (1997) Comm. Math. Phys. , vol.183 , Issue.1 , pp. 23-54
  • 29
    • 0031524343 scopus 로고    scopus 로고
    • Casson-Walker invariant of Seifert fibered rational homology spheres as quantum SO(3)-invariant
    • G. Sato, Casson-Walker invariant of Seifert fibered rational homology spheres as quantum SO(3)-invariant, J. Knot Theory Ramifications 6 (1997), no. 1, 79-93.
    • (1997) J. Knot Theory Ramifications , vol.6 , Issue.1 , pp. 79-93
    • Sato, G.1
  • 30
    • 0037570308 scopus 로고    scopus 로고
    • Lectures on the topology of 3-manifolds. An introduction to the Casson invariant
    • Walter de Gruyter, Berlin
    • N. Saveliev, Lectures on the Topology of 3-Manifolds. An Introduction to the Casson Invariant, de Gruyter Textbook, Walter de Gruyter, Berlin, 1999.
    • (1999) De Gruyter Textbook
    • Saveliev, N.1
  • 31
    • 0003332777 scopus 로고
    • An extension of Casson's invariant
    • Princeton University Press, New Jersey
    • K. Walker, An Extension of Casson's Invariant, Annals of Mathematics Studies, vol. 126, Princeton University Press, New Jersey, 1992.
    • (1992) Annals of Mathematics Studies , vol.126
    • Walker, K.1
  • 32
    • 14644388676 scopus 로고
    • Quantum field theory and the Jones polynomial
    • E. Witten, Quantum field theory and the Jones polynomial, Comm. Math. Phys. 121 (1989), no. 3, 351-399.
    • (1989) Comm. Math. Phys. , vol.121 , Issue.3 , pp. 351-399
    • Witten, E.1
  • 33
    • 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), no. 5, 945-960.
    • (2001) Topology , vol.40 , Issue.5 , pp. 945-960
    • Zagier, D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.