References
J. Conway, “Advanced problem 5327,” Amer. Math. Monthly,72, 915 (1965).
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.)
H. Helling, A. C. Kim, and J. L. Mennicke, “A geometric study of Fibonacci groups,” J. Lie Theory,8, No. 1, 1–23 (1998).
B. Zimmermann, “On the Hantzsche-Wendt manifold,” Monatsh. Math.,110, No. 3-4, 321–327 (1990).
A. Yu. Vesnin and A. D. Mednykh, “Hyperbolic volumes of Fibonacci manifolds,” Sibirsk. Mat. Zh.,36, No. 2, 266–277 (1995).
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. 169–184
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).
C. Maclachlan and A. W. Reid, “Generalised Fibonacci manifolds,” Transformation Groups,2, No. 2, 165–182 (1997).
R. Benedetti and C. Petronio, Lectures on Hyperbolic Geometry, Springer-Verlag, Berlin (1992).
N. Kuiper, “Fairly symmetric hyperbolic manifolds,” in: Geometry and Topology of Submanifolds, II (Avignon, 1988), World Sci. Publishing, Teaneck, NJ, 1990, pp. 165–204.
D. McCullough, “Automorphisms of punctured-surface bundles,” in: Geometry and Topology, 1987,105, pp. 179–211.
A. Borel, “Commensurability classes and hyperbolic volumes,” Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4),8, 1–33 (1991).
A. Mednykh and A. Rasskazov, On the Structure of the Canonical Fundamental Set for the 2-Bridge Link Orbifolds [Preprint 98-062], University of Bielefeld (1998).
F. M. Gehring and G. J. Martin, “Commutators, collars and the geometry of Möbius groups,” J. D'Anal. Math.,63, 175–219 (1994).
A. D. Mednykh, “Groups of automorphisms of three-dimensional hyperbolic manifolds,” Dokl. Akad. Nauk SSSR,285, No. 1, 40–44 (1985).
A. D. Mednykh and A. Yu. Vesnin, “On three-dimensional hyperbolic manifolds of Löbell type,” in: Complex Analysis and Applications'85 (Varna, 1985), Publ. House of the Bulgarian Acad. Sci., Sofia, 1986, pp. 40–44.
A. D. Mednykh, “The isometry group of the hyperbolic space of a Seifert-Weber dodecahedron,” Sibirsk. Mat. Zh.,28, No. 5, 134–144 (1987).
H. S. M. Coxeter and W. O. J. Moser, Generators Relations for Discrete Groups [Russian translation], Nauka, Moscow (1980).
M. Dehn, “Dei beiden Kleeblattschlingen,” Math. Ann., Bd. 75, 402–413 (1914).
W. Magnus, “Untersuchungen über einige unendliche diskontinuierliche Gruppen,” Math. Ann., Bd. 105, 52–74 (1931).
R. H. Crowell and R. H. Fox, Introduction to Knot Theory [Russian translation], Mir, Moscow (1967).
A. Haefliger and N. D. Quach, “Appendice: une presentation de groupe fundamental d'une orbifold,” Astérisque,116, 98–107 (1984).
J. Hempel, “The lattice of branched covers over the figure-eight knot,” Topology Appl.,34, No. 2, 183–201 (1990).
J. Minkus, “The branched cyclic coverings of 2-bridge knots and links,” Mem. Amer. Math. Soc.,35, No. 255, 1–67 (1982).
J. G. Ratcliffe, Foundations of Hyperbolic Manifolds, Graduate Texts in Mathematics. Vol. 149, Springer-Verlag, Berlin (1994).
W. P. Thurston, the Geometry and Topology of Three-Manifolds, Princeton Univ. Press, Princeton (1980).
K. Wolcott, “The knotting of theta curves and other graphs in\(\mathbb{S}^3 \),” in: Geometry and Topology, 1987,105, 325–346.
K. Morimoto and M. Sakuma, “On unknotting tunnels for knots,” Math. Ann.,289, 143–167 (1991).
Additional information
The research was supported by the Russian Foundation for Basic Research (Grants 98-01-00699 and 96-01-01523).
Novosibirsk. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 40, No. 1, pp. 14–29, January–February, 1999.
Rights and permissions
About this article
Cite this article
Vesnin, A.Y., Rasskazov, A.A. Isometries of hyperbolic Fibonacci manifolds. Sib Math J 40, 9–22 (1999). https://doi.org/10.1007/BF02674286
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02674286