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Fractional Fibronacci groups and manifolds

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References

  1. J. Conway, “Advanced problem 5327,” Amer. Math. Monthly,72, 915 (1965).

    Article  MathSciNet  Google Scholar 

  2. J. Conway, “Solution to Advanced problem 5327,” Amer. Math. Monthly,74, 91–93 (1967).

    Article  MathSciNet  Google Scholar 

  3. G. Havas, “Computer aided determination of a Fibonacci group,” Bull. Austral. Math. Soc.,15, 297–305 (1976).

    Article  MATH  MathSciNet  Google Scholar 

  4. M. F. Newman, “Proving a group infinite,” Arch. Math.,54, No. 3, 209–211 (1990).

    Article  MATH  MathSciNet  Google Scholar 

  5. R. M. Thomas, “The Fibonacci groupsF(2,2m),” Bull. London Math. Soc.,21, No. 5, 463–465 (1989).

    Article  MATH  MathSciNet  Google Scholar 

  6. D. L. Johnson, “Extensions of Fibonacci groups,” Bull. London Math. Soc.,7, 101–104 (1974).

    Article  Google Scholar 

  7. R. M. Thomas, “The Fibonacci groups revisited,” in: Groups St Andrews 1989, Cambridge Univ. Press, Cambridge, 1991,2, pp. 445–456. (London Math. Soc. Lecture Notes Ser.;160.)

    Google Scholar 

  8. C. Maclachlan, “Generalizations of Fibonacci numbers, groups and manifolds,” in: Combinatorial and Geometric Group Theory, Edinburgh, 1993, Cambridge Univ. Press, Cambridge, 1995, pp. 233–238. (London Math. Soc. Lecture Notes Ser.;204.)

    Google Scholar 

  9. C. Maclachlan and A. W. Reid, “Generalised Fibonacci manifolds,” Transform. Groups,2, No. 2, 165–182 (1997).

    Article  MATH  MathSciNet  Google Scholar 

  10. H. Helling, A. C. Kim, and J. L. Mennicke, “A geometric study of Fibonacci groups,” J. Lie Theory,8, No. 1, 1–23 (1988).

    MathSciNet  Google Scholar 

  11. J. L. Mennicke, “On Fibonacci groups and some other groups,” in: Proceedings of the First International Conference on Group Theory (Groups—Korea 1988), Held in Pusan, Korea, August 15–21, 1988. Springer-Verlag, Berlin, 1989, pp. 117–123. (Lecture Notes in Math.;1398.)

    Google Scholar 

  12. B. Zimmermann. “On the Hantzsche-Wendt manifold,” Monatsh. Math.,110, No. 3-4, 321–327 (1990).

    Article  MATH  MathSciNet  Google Scholar 

  13. H. M. Hilden, M. T. Lozano, and J. M. Montesinos-Amilibia, “The arithmeticity of the figure eight knot orbifolds.” in: Topology'90 (Columbus, OH, 1990), Ohio State Univ. Math. Res. Inst. Publ., 1. de Gruyter, Berlin, 1992, pp. 169–183.

    Google Scholar 

  14. A. Cavicchioli and F. Spaggiari. “The classification of 3-manifolds with spines related to Fibonacci groups,” in: Algebraic Topology. Homotopy and Group Coliomology. Springer-Verlag, Berlin. 1992, pp. 50–78. (Lecture Notes in Math.;1509.)

    Chapter  Google Scholar 

  15. A. Yu. Vesnin and A. D. Mednykh, “Fibonacci manifolds as two-fold coverings of the three-dimensional sphere and the Meyerhoff-Neumann conjecture,” Sibirsk. Mat. Zh.,37, No. 5, 534–542 (1996).

    Google Scholar 

  16. W. P. Thurston, The Geometry and Topology of Three-Manifolds, Princeton Univ. Press. Princeton (1980).

    Google Scholar 

  17. M. Takahashi, “On the presentations of the fundamental groups of 3-manifolds,” Tsukuba J. Math.,13, No. 1, 175–189 (1989).

    MATH  MathSciNet  Google Scholar 

  18. J. Weeks, “SnapPea” (the program and accompanying documentation are available by ftp from geom.umn.edu).

  19. G. Burde and H. Zieschang, Knots, Walter de Gruyter and Co., Berlin and New York (1985).

    MATH  Google Scholar 

  20. J. M. Montesinos, “Surgery on links and double branched covers of\(\mathbb{S}^3 \),” in: Knots, Groups, and 3-Manifolds, Princeton Univ. Press, Princeton, 1975, pp. 227–259.

    Google Scholar 

  21. J. H. Conway, “An enumeration of knots and links and some of their algebraic properties,” in: Computational Problems in Abstract Algebra, Pergamon Press, Oxford, 1970, pp. 329–358. (Proc. Conf. Oxford, 1967.)

    Google Scholar 

  22. A. Haefliger and N. D. Quach, “Appendice: une presentation du groupe fundamental d'une orbifold,” Astérisque,116, 98–107 (1984).

    Google Scholar 

  23. H. M. Hilden, M. T. Lozano, and J. M. Montesinos-Amilibia, “On the arithmetic 2-bridge knots and link orbifolds and a new knot invariant,” J. Knot Theory Ramifications,4, No. 1, 81–114 (1995).

    Article  MATH  MathSciNet  Google Scholar 

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Additional information

The authors are thankful for support to the Korean Science and Engineering Foundation KOSEF (Grant 96-0701-03-01-3) and the Russian Foundation for Basic Research (Grants 95-01-01410 and 98-01-00699).

Novosibirsk. Pusan. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 39. No. 4, pp. 765–775, July–August, 1998.

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Vesnin, A.Y., Kim, A.C. Fractional Fibronacci groups and manifolds. Sib Math J 39, 655–664 (1998). https://doi.org/10.1007/BF02673051

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