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1998 | 42 | 1 | 205-220
Tytuł artykułu

Finite type invariants of integral homology 3-spheres: A survey

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Rocznik
Tom
42
Numer
1
Strony
205-220
Opis fizyczny
Daty
wydano
1998
Twórcy
  • Department of Mathematics, University of California, Riverside, California 92521, U.S.A.
Bibliografia
  • [1] S. Akbulut and J. McCarthy, Casson's invariant for oriented homology 3-spheres: An exposition, Math. Notes, vol. 36, Princeton University Press, 1990.
  • [2] D. Bar-Natan, Perturbative aspects of the Chern-Simons topological quantum field theory, Ph. D. Thesis, Princeton University, 1991. Appeared as Perturbative Chern-Simons theory, Jour. Knot Theory Rami., 14(1995).
  • [3] D. Bar-Natan, On the Vassiliev knot invariants, Topology, 34(1995).
  • [4] D. Bar-Natan, Polynomial invariants are polynomial, Math. Res. Letter, 2(1995).
  • [5] D. Bar-Natan and S. Garoufalidis, On the Melvin-Morton-Rozansky conjecture, preprint, 1994.
  • [6] J. Birman and X.-S. Lin, Knot polynomials and Vassiliev invariants, Invent. Math., 111(1993)
  • [7] S. Garoufalidis, On finite type 3-manifold invariants I, to appear in Jour. of Knot Theory Rami.
  • [8] S. Garoufalidis and J. Levine, On finite type 3-manifold invariants II, preprint, June 1995.
  • [9] S. Garoufalidis and J. Levine, On finite type 3-manifold invariants IV: comparison of definitions, preprint, September 1995.
  • [10] S. Garoufalidis and J. Levine, Finite type 3-manifold invariants, the mapping class group and blinks, preprint, March 1996.
  • [11] S. Garoufalidis and T. Ohtsuki, On finite type 3-manifold invariants III: manifold weight systems, preprint, August 1995.
  • [12] S. Garoufalidis and T. Ohtsuki, On finite type 3-manifold invariants V: rational homology 3-Spheres, preprint, preprint, November 1995.
  • [13] M. Greenwood and X.-S. Lin, On Vassiliev knot invariants induced from finite type 3-manifold invariants, preprint, May 1995.
  • [14] M. Gusarov, On n-equivalence of knots and invariants of finite degree, Adv. in Sov. Math., 18(1994).
  • [15] N. Habegger, Finite type 3-manifold invariants: a proof of a conjecture of Garoufalidis, preprint, July 1995.
  • [16] G. Hardy and E. Wright, An introduction to the theory of numbers, Oxford University Press, Fifth Edition, 1979.
  • [17] J. Hoste, A formula for Casson's invariant, Tran. AMS, 297(1986).
  • [18] V. Jones, Hecke algebra representations of braid groups and link polynomials, Ann. of Math., (2)186(1987).
  • [19] L. Kauffman, The Conway polynomial, Topology, 20(1981).
  • [20] R. Kirby and P. Melvin, The 3-manifold invariants of Witten and Reshetikhin-Turaev for sl(2,ℂ), Invent. Math., 105(1991).
  • [21] M. Kontsevich, Vassiliev's knot invariants, Adv. in Sov. Math., 16(1993).
  • [22] R. Lawrence, Asymptotic expansion of Witten-Reshetikhin-Turaev invariants for some simple 3-manifolds, to appear in Jour. of Math. Phys.
  • [23] T. Q. T. Le and J. Murakami, Representations of the category of tangles by Kontsevich's iterated integral, Comm. in Math. Phys., 168(1995).
  • [24] T. Q. T. Le, An invariant of integral homology 3-spheres which is universal for all finite type invariants, preprint, January 1996.
  • [25] T. Q. T. Le, J. Murakami and T. Ohtsuki, On a universal invariant of 3-manifolds, preprint, December 1995.
  • [26] T. Q. T. Le, H. Murakami, J. Murakami and T. Ohtsuki, A three-manifold invariant derived from the universal Vassiliev-Kontsevich invariant, Proc. Japan Acad., Ser. A, 71(1995).
  • [27] J. Levine, Surgery on links and the $\bar μ$-invariants, Topology, 26(1987).
  • [28] X.-S. Lin, Finite type link invariants of 3-manifolds, Topology, 33(1994).
  • [29] X.-S. Lin and Z. Wang, Integral geometry of plane curves and knot invariants, to appear in Jour. of Diff. Geom.
  • [30] X.-S. Lin and Z. Wang, On Ohtsuki's invariants of integral homology 3-spheres I, preprint, September 1995.
  • [31] X.-S. Lin and Z. Wang, On Ohtsuki's invariants of integral homology 3-spheres II, in preparation.
  • [32] W. B. R. Lickorish, Three-manifold invariants and the Temperley-Lieb algebra, Math. Ann., 209(1991).
  • [33] P. Melvin and H. Morton, The coloured Jones function, Comm. Math. Phys., 169(1995).
  • [34] J. Milnor and J. Moore, On the structure of Hopf algebras, (2)81(1965).
  • [35] S. Morita, Casson's invariant for homology 3-spheres and characteristic classes of vector bundles, Topology, 28(1989).
  • [36] S. Morita, On the structure of Torelli group and the Casson invariant, Topology, 30(1991).
  • [37] H. Murakami, Quantum SU(2)-invariants dominate Casson's SU(2)-invariant, Math. Proc. Camb. Phil. Soc., 115(1994).
  • [38] T. Ohtsuki, A polynomial invariant of integral homology 3-spheres, Math. Proc. Camb. Phil. Soc., 117(1995).
  • [39] T. Ohtsuki, Finite type invariants of integral homology 3-spheres, to appear in Jour. of Knot Theory Rami.
  • [40] J. Przytycki, Vassiliev-Gusarov skein modules of 3-manifolds and criteria for periodicity of knots, in Low-Dimensional Topology (ed. K. Johannson), International Press Co., 1994.
  • [41] L. Rozansky, The trivial connection contributions to Witten's invariants of rational homology spheres, preprint, 1995.
  • [42] L. Rozansky, Witten's invariants of rational homology spheres at prime values of K and trivial connection contribution, preprint, 1995.
  • [43] L. Rozansky, On p-adic convergence of perturbative invariants of some rational homology spheres, preprint, 1996.
  • [44] N. Y. Reshetikhin and V. G. Turaev, Invariants of 3-manifolds via link polynomials and quantum groups, Invent. Math., 103(1991).
  • [45] T. Stanford, Finite type invariants of knots, links, and graphs, to appear in Topology.
  • [46] T. Stanford, Braid commutators and Vassiliev invariants, to appear in Paci. Jour. of Math.
  • [47] V. A. Vassiliev, Cohomology of knot spaces, in Theory of Singularities and its Applications (ed. V. Arnold), AMS, 1990.
  • [48] K. Walker, An extension of Casson's invariant, Ann. Math. Studies, vol. 121, Princeton Univ. Press, 1991.
Typ dokumentu
Bibliografia
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