Skip to main content
Log in

Hyperbolic volumes of Fibonacci manifolds

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  5. H. Helling, A. C. Kim, and J. Mennicke, A Geometric Study of Fibonacci Groups [Preprint/SFB-343, Diskrete Strukturen in der Mathematik], Bielefeld (1990).

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

    Google Scholar 

  7. D. L. Johnson, J. W. Wamsley, and D. Wright, “The Fibonacci groups,” Proc. London Math. Soc.,29, 577–592 (1974).

    Google Scholar 

  8. H. M. Hilden, M. T. Lozano, and J. M. Montesinos, “The arithmeticity of the figure eight knot orbifolds,” in: Topology'90, Contrib. Res. Semester Low Dimensional Topology, Columbus/OH (USA) 1990, Ohio State Univ. Math. Res. Inst. Publ., 1992, pp. 169–183.

    Google Scholar 

  9. J. Hempel, “The lattice of branched covers over the figure-eight knot,” Topology Appl.,34, No. 2, 183–201 (1990).

    Google Scholar 

  10. S. V. Matveev and A. T. Fomenko, “Constant energy surfaces of Hamiltonian systems, enumeration of three-dimensional manifolds in increasing order of complexity, and computation of volumes of closed hyperbolic manifolds,” Uspekhi Mat. Nauk,43, No. 1, 5–22 (1988).

    Google Scholar 

  11. J. Weeks, Hyperbolic Structures on 3-Manifolds, Ph. D. Thesis, Princeton Univ., Princeton (1985).

    Google Scholar 

  12. W. P. Thurston, The Geometry and Topology of Three-Manifolds, Princeton Univ., Princeton (1980) (Lecture Notes in Math.).

    Google Scholar 

  13. R. Meyerhoff and W. D. Neumann, “An asymptotic formula for the eta invariants of hyperbolic 3-manifolds,” Comment. Math. Helv.,67, 28–46 (1992).

    Google Scholar 

  14. D. Rolfsen, Knots and Links, Publish or Perish Inc., Berkeley, Ca. (1976).

    Google Scholar 

  15. J. Milnor, “Hyperbolic geometry: the first 150 years,” Bull. Amer. Math. Soc., V. 6. P. 9–25 (1982).

    Google Scholar 

  16. È. B. Vinberg, “Volumes of non-Euclidean polyhedrons,” Uspekhi Mat. Nauk,48, No. 2, 17–46 (1993).

    Google Scholar 

  17. W. D. Neumann and D. Zagier, “Volumes of hyperbolic three-manifolds,” Topology,24, No. 3, 307–322 (1985).

    Google Scholar 

  18. R. H. Crowell and R. H. Fox, Introduction to Knot Theory, Ma.: Ginn and Co., Boston (1963).

    Google Scholar 

  19. A. Borel, “Commensurability classes and hyperbolic volumes,” Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4),8, 1–33 (1991).

    Google Scholar 

  20. A. W. Reid, “Arithmeticity of knot complements,” J. London Math. Soc. (2),43, No. 1, 171–184 (1991).

    Google Scholar 

  21. R. Riley, “An elliptical path from parabolic representations to hyperbolic structures,” Lecture Notes in Math.,722, 99–133 (1979).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Sibirskiĩ Matematicheskiĩ, Vol. 36, No. 2, pp. 266–277, March–April, 1995.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vesnin, A.Y., Mednykh, A.D. Hyperbolic volumes of Fibonacci manifolds. Sib Math J 36, 235–245 (1995). https://doi.org/10.1007/BF02110146

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02110146

Keywords

Navigation