Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Monodromy Maps of Fibered 2-Bridge Knots as Elements in Automorphism Groups of Free Groups

  • Goda, Hiroshi (Department of Mathematics, Tokyo University of Agriculture and Technology) ;
  • Suzuki, Masaaki (Department of Frontier Media Science, Meiji University)
  • Received : 2014.07.21
  • Accepted : 2015.02.21
  • Published : 2016.09.23
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Abstract

In this note, we study a monodromy map of a fibered 2-bridge knot. We show the monodromy map of a fibered 2-bridge knot as an element in the automorphism group of a free group.

Keywords

References

  1. J. C. Cha and C. Livingston, KnotInfo, Table of knot invariants, http://www.indiana.edu/knotinfo/.
  2. R. Crowell, Genus of alternating link types, Ann. of Math. 69(2)(1959), 258-275. https://doi.org/10.2307/1970181
  3. S. Fukuhara, Explicit formulae for two-bridge knot polynomials, J. Aust. Math. Soc. 78(2005), 149-166. https://doi.org/10.1017/S1446788700008004
  4. D. Gabai and W.H. Kazez, Pseudo-Anosov maps and surgery on bred 2 -bridge knots, Topology Appl. 37(1990), 93-100. https://doi.org/10.1016/0166-8641(90)90018-W
  5. A. Hatcher and W. Thurston, Incompressible surfaces in 2-bridge knot complements, Invent. Math. 79(1985), 225-246. https://doi.org/10.1007/BF01388971
  6. T. Kanenobu, Alexander polynomials of two-bridge links, J. Austral. Math. Soc. Ser. A 36(1984), 59-68. https://doi.org/10.1017/S1446788700027336
  7. J. Milnor, In nite cyclic coverings, 1968 Conference on the Topology of Manifolds (Michigan State Univ., E. Lansing, Mich., 1967), 115-133.
  8. K. Morimoto and M. Sakuma, On unknotting tunnels for knots, Math. Ann. 289(1991), 143-167. https://doi.org/10.1007/BF01446565
  9. K. Murasugi, On the genus of the alternating knot. I, II, J. Math. Soc. Japan 10(1958), 94-105, 235-248. https://doi.org/10.2969/jmsj/01010094
  10. K. Murasugi, Signatures and Alexander polynomials of two-bridge knots, C. R. Math. Rep. Acad. Sci. Canada 5(1983), 133-136.
  11. D. Rolfsen, Knots and links, Mathematics Lecture Series, No. 7. Publish or Perish, Inc., Berkeley, Calif., 1976.
  12. H. Zieschang, E. Vogt and H. Coldewey, Surfaces and planar discontinuous groups, Lecture Notes in Mathematics, 835. Springer, Berlin, 1980.