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1998 | 42 | 1 | 275-295
Tytuł artykułu

3-coloring and other elementary invariants of knots

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Rocznik
Tom
42
Numer
1
Strony
275-295
Opis fizyczny
Daty
wydano
1998
Twórcy
  • Department of Mathematics, George Washington University, Washington, D.C. 20052, U.S.A.
Bibliografia
  • [A-B] J. W. Alexander, G. B. Briggs, On types of knotted curves, Ann. of Math 28 (1926/27), 562-586.
  • [Bruc] R. H. Bruck, A survey of binary systems, Springer, Berlin 1958.
  • [Br] H. Brunn, Topologische Betrachtungen, Zeitschrift für Mathematik und Physik, 37 (1892), 106-116.
  • [B-Z] G. Burde, H. Zieschang, Knots, De Gruyter (1985).
  • [C-F] R. H. Crowell, R. H. Fox, An introduction to knot theory, Ginn and Co., 1963.
  • [Cox] H. S. M. Coxeter, Factor groups of the braid group, Proc. Fourth Canadian Math. Congress, Banff, 1957, 95-122.
  • [F-R] R. Fenn, C. Rourke, Racks and links in codimension two, Journal of Knot Theory and its Ramifications, 1(4) 1992, 343-406.
  • [F-1] R. H. Fox, A quick trip through knot theory, In: Top. 3-manifolds, Proc. 1961 Top. Inst. Univ. Georgia (ed. M. K. Fort, jr), 120-167. Englewood Cliffs. N. J.: Princeton-Hall, 1962.
  • [F-2] R. H. Fox, Metacyclic invariants of knots and links, Canadian J. Math., XXII(2) 1970, 193-201.
  • [Ga] C. F. Gauss, Zur mathematischen Theorie der electrodynamischen Wirkungen, 1833, Werke, Königliche Gesellschaft der Wissenschaften zu Göttingen, 5 (1877), 602-629.
  • [G-J] D. Goldschmidt, V. F. R. Jones, Metaplectic link invariants, Geometriae Dedicata, 31 (1989), 165-191.
  • [Goe] L. Goeritz, Knoten und quadratische Formen, Math. Z., 36(1933), 647-654.
  • [Gor] C. McA. Gordon, Some aspects of classical knot theory, In: Knot theory, L. N. M. 685 (1978) 1-60.
  • [H-U] T. Harikae, Y. Uchida, Irregular dihedral branched coverings of knots, in Topics in knot theory, N. A. T. O. A. S. I. series C, 399, (ed. M. Bozhüyük) Kluwer Academic Publisher (1993), 269-276.
  • [H-J] P. de la Harpe, V. F. R. Jones, Graph invariants related to statistical mechanical models: Examples and Problems, J. Combinat. Theory B., 57, 1993, 207-227.
  • [J-P] W. Jakobsche, J. H. Przytycki, Topologia 3-wymiarowych rozmaitości, Wydawnictwa Uniwersytetu Warszawskiego, 1987.
  • [Ja] F. Jaeger, Composition products and models for the Homfly polynomial, L'Enseignement Mathématique, 35 (1989), 323-361.
  • [Ja-P] F. Jaeger, J. H. Przytycki, A non-commutative version of the Goeritz matrix of a link, in preparation.
  • [Jo-1] V. F. R. Jones, On knot invariants related to some statistical mechanics models, Pacific J. Math., 137(2), 1989, 311-334.
  • [Jo-2] V. F. R. Jones, Subfactors and knots, CBMS, Regional Conference Series in Mathematics 80, AMS 1991.
  • [Joy] D. Joyce, A classifying invariant of knots: the knot quandle, Jour. Pure Appl. Alg., 23 (1982), 37-65.
  • [K] L. H. Kauffman, Knots and Physics, Series on Knots and Everything - Vol. 1, World Scientific, 1991.
  • [Li] W. B. R. Lickorish, Polynomials for links. Bull. London Math. Soc. 20 (1988) 558-588.
  • [L-M] W. B. R. Lickorish, K. Millett, Some evaluations of link polynomials, Comment. Math. Helv., 61(1986), 349-359.
  • [Liv] C. Livingston, Knot theory, The Carus Math. Monographs, Vol 24, MAA 1993.
  • [Mon] J. M. Montesinos, Lectures on 3-fold simple coverings and 3-manifolds, Contemporary Mathematics 44 (Combinatorial methods in topology and algebraic geometry), 1985, 157-177.
  • [Mo] H. R. Morton, Problems, in Braids, Ed. J. S. Birman, A. Libgober, AMS Contemporary Math., 78(1988), 557-574.
  • [Mur] H. Murakami, Unknotting number and polynomial invariants of a link, preprint 1985.
  • [Nak] Y. Nakanishi, On generalized unknotting operations, J. Knot Theory and its Ramifications, 3(2), 1994, 197-209.
  • [P-1] J. H. Przytycki, Elementary conjectures in classical knot theory, in Quantum Topology, Ed. L. J. Kauffman, R. A. Baadhio, Series on Knots and Everything - Vol. 3, World Scientific, 1993, 292-320.
  • [P-2] J. H. Przytycki, $t_k$-moves on links, In Braids, ed. J. S. Birman and A. Libgober, Contemporary Math. Vol. 78 (1988) 615-656.
  • [Re] K. Reidemeister, Elementare Begründung der Knotentheorie, Abh. Math. Sem. Univ. Hamburg, 5 (1927), 24-32.
  • [Re-1] K. Reidemeister, Knotentheorie. Ergebn. Math. Grenzgeb., Bd. 1; Berlin: Springer-Verlag (1932) (English translation: Knot theory, BSC Associates, Moscow, Idaho, USA, 1983).
  • [Rol] D. Rolfsen, Knots and links, Publish or Perish, 1976.
  • [R-T-1] N. Reshetikhin, V. Turaev, Ribbon graphs and their invariants derived from quantum groups, Jour. Commun. Math. Phys., 127 (1990), 1-26.
  • [R-T-2] N. Y. Reshetikhin, V. Turaev, Invariants of three manifolds via link polynomials and quantum groups. Invent. Math. 103 (1991) 547-597.
  • [S-W] D. Silver, S. G. Williams, Generalized n-Colorings of Links, this volume.
  • [Tu-1] V. G. Turaev, The Yang-Baxter equation and invariants of links, Invent. Math., 92(1988), 527-553.
  • [T-V] V. G. Turaev, O. Y. Viro, State sum invariants of 3-manifolds and quantum 6j-symbols, Topology, 31 (1992), 865-902.
  • [Wa] M. Wada, Group invariants of links, Topology 31(2) 1992.
  • [Wi] W. Wirtinger, Über die Verzweigungen bei Funktionen von zwei Veränderlichen, Jahresbericht d. Deutschen Mathematiker Vereinigung, 14 (1905), 517. (The title of the talk supposedly given at September 26 1905 at the annual meeting of the German Mathematical Society in Meran).
  • [Wu] F. Y. Wu, Knot theory and statistical mechanics, Review of modern physics, 64(4), October 1992, 1099-1131.
Typ dokumentu
Bibliografia
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