Skip to main content
Log in

Surgery on Small Volume Hyperbolic 3-Orbifolds

  • 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. Hodgson C. D. and Weeks J. R., “Symmetries, isometries and length spectra of closed hyperbolic three-manifolds,” Experiment. Math., 3, No. 4, 261-274 (1994).

    Google Scholar 

  2. Mednykh A. and Vesnin A., “Covering properties of small volume hyperbolic 3-manifolds,” J. Knot Theory Ramifications, 7, No. 3, 381-392 (1998).

    Google Scholar 

  3. Dunbar W. and Meyerhoff R., “Volumes of hyperbolic 3-orbifolds,” Indiana Univ. Math. J., 43, 611-637 (1994).

    Google Scholar 

  4. Adams C. C., “Limit volumes of hyperbolic 3-orbifolds,” J. Differential Geom., 34, 115-141 (1991).

    Google Scholar 

  5. Thurston W. P., The Geometry and Topology of 3-Manifolds, Princeton, Princeton Univ. (1978).

    Google Scholar 

  6. Neumann W. D. and Reid A. W., “Notes on Adams' small volume orbifolds,” in: Topology '90(eds. B. Apanasov, W. D. Neumann, A. W. Reid, and L. Siebenmann), Ohio State University Mathematical Research Institute Publications 1, de Gruyter, Berlin, 1992, pp. 311-314.

    Google Scholar 

  7. Brunner A., Frame M., Lee Y., and Wielenberg N., “Classifying torsion-free subgroups of the Picard group,” Trans. Amer. Math. Soc., 282, 205-235 (1984).

    Google Scholar 

  8. Hatcher A., “Hyperbolic structures of arithmetic type on some link complements,” J. London Math. Soc. (2), 27, 345-355 (1983).

    Google Scholar 

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

    Google Scholar 

  10. Adams C., Hildebrand M., and Weeks J., “Hyperbolic invariants of knots and links,” Trans. Amer. Math. Soc., 326, 1-56 (1991).

    Google Scholar 

  11. Frohman C. and Fine B., “Some amalgam structures for Bianchi groups,” Proc. Amer. Math. Soc., 102, 221-229 (1988).

    Google Scholar 

  12. Hatcher A., Bianchi Orbifolds of Small Discriminant [Preprint], available from the author's homepage (1990).

  13. Grunewald F. and Hirsch U., “Link complements arising from arithmetic group actions,” Internat. J. Math., 6, 337-370 (1995).

    Google Scholar 

  14. Kerckhoff S. P., “Deformations of hyperbolic cone manifolds,” in: Proc. 37th Taniguichi Sympos. on Topology and Teichmüller spaces, Finland, July 1995, ed. by S. Kojima et al., World Sci. Publ. Co., Singapore, 1996, pp. 101-114.

    Google Scholar 

  15. Kojima S., “Hyperbolic 3-manifolds singular along knots,” Chaos Solitons Fractals, 9, No. 4-5, 765-777 (1998).

    Google Scholar 

  16. Dunbar W., “Geometric orbifolds,” Rev. Mat. Univ. Complut. Madrid, 1, No. 1, 67-99 (1988).

    Google Scholar 

  17. Conway J. H., “An enumeration of knots and links, and some of their algebraic properties,” in: Computational Problems in Abstract Algebra (ed. J. Leach), Pergamon Press, New York, 1969, pp. 329-364.

    Google Scholar 

  18. Boileau M. and Zimmermann B., “The π-orbifold group of a link,” Math. Z., 200, No. 2, 187-208 (1989).

    Google Scholar 

  19. Zimmermann B., “On the Hantzsche-Wendt manifold,” Monatsh. Math., 110, 321-327 (1990).

    Google Scholar 

  20. Wolcott K., “The knotting of theta curves and other graphs in S3,” in: Geometry and Topology (eds. McCrory and Shifrin), Marcel Dekker, New York, 1987, pp. 325-346.

    Google Scholar 

  21. Nakao M., “On the ℤ2 ⊕ ℤ2 branched coverings of spatial K4-graphs,” in: Knots 90 (ed. A. Kawauchi), de Gruyter, Berlin, 1992, pp. 103–116.

    Google Scholar 

  22. Zimmermann B., “On hyperbolic knots with the same m-fold and n-fold cyclic branched coverings,” Topology Appl., 79, 143-157 (1997).

    Google Scholar 

  23. Vesnin A. Yu. and Mednykh A. D., “Three-dimensional hyperelliptic manifolds and hamiltonian graphs,” Sibirsk. Mat. Zh., 40, No. 5, 1035-1051 (1999).

    Google Scholar 

  24. Petrov V., Dehn Surgery on Hyperbolic Orbifolds [Preprint], available from the author's homepage (1999).

  25. Zimmermann B., “Genus actions of finite groups on 3-manifolds,” Michigan Math. J., 43, 593-610 (1996).

    Google Scholar 

  26. Zimmermann B., “On a hyperbolic 3-manifold with some special properties,” Math. Proc. Cambridge Philos. Soc., 113, 87-90 (1993).

    Google Scholar 

  27. Takahashi M., “On the presentation of the fundamental group of 3-manifolds,” Tsukuba J. Math., 13, 175-189 (1989).

    Google Scholar 

  28. Vesnin A. Yu. and Kim A. C., “Fractional Fibonacci groups and manifolds,” Sibirsk. Mat. Zh., 39, No. 4, 765-775 (1998).

    Google Scholar 

  29. Ruini B. and Spaggiari F., “On the structure of Takahashi manifolds,” Tsukuba J. Math., 22, 723-739 (1998).

    Google Scholar 

  30. Burde G. and Zieschang H., Knots, De Gruyter Stud. Math. 5, Berlin and New York (1985).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vesnin, A.Y., Mednykh, A.D. & Zimmermann, B. Surgery on Small Volume Hyperbolic 3-Orbifolds. Siberian Mathematical Journal 42, 271–281 (2001). https://doi.org/10.1023/A:1004884912927

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1004884912927

Keywords

Navigation