Skip to main content
SpringerLink
Log in

Torus Knots and Dunwoody Manifolds

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

We obtain an explicit representation as Dunwoody manifolds of all cyclic branched coverings of torus knots of type (p,mp±1), with p > 1 and m > 0.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Cavicchioli A., Hegenbarth F., and Kim A. C., “A geometric study of Sieradski groups,” Algebra Colloq., 5,No. 2, 203-217 (1998).

    Google Scholar 

  2. Dunwoody M. J., “Cyclic presentations and 3-manifolds,” in: Proc. Inter. Conf., Groups-Korea 94, Walter de Gruyter, Berlin and New York, 1995, pp. 47-55.

  3. Helling H., Kim A. C., and Mennicke J. L., “A geometric study of Fibonacci groups,” J. Lie Theory, 8, 1-23 (1998).

    Google Scholar 

  4. Kim A. C., “On the Fibonacci group and related topics,” Contemp. Math., 184, 231-235 (1995).

    Google Scholar 

  5. Kim A. C., Kim Y., and Vesnin A. “On a class of cyclically presented groups,” in: Proc. Inter. Conf., Groups-Korea 98, Walter de Gruyter, Berlin; New York, 2000, pp. 211-220.

  6. Maclachlan C. and Reid A. W., “Generalised Fibonacci manifolds,” Transform. Groups, 2, 165-182 (1997).

    Google Scholar 

  7. Vesnin A. and Kim A. C., “The fractional Fibonacci groups and manifolds,” Siberian Math. J., 39, 655-664 (1998).

    Google Scholar 

  8. Grasselli L. and Mulazzani M., “Genus one 1-bridge knots and Dunwoody manifolds,” Forum Math., 13, 379-397 (2001).

    Google Scholar 

  9. Cattabriga A. and Mulazzani M., “Strongly-cyclic branched coverings of (1,1)-knots and cyclic presentations of groups,” Math. Proc. Cambridge Philos. Soc., 135, 137-146 (2003).

    Google Scholar 

  10. Kawauchi A., A Survey of Knot Theory, Birkhäuser-Verlag, Basel (1996).

    Google Scholar 

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

    Google Scholar 

  12. Johnson D. L. Topics in the Theory of Group Presentations, Cambridge Univ. Press, Cambridge (1980). (London Math. Soc. Lecture Note Ser.; 42.)

    Google Scholar 

  13. Cattabriga A. and Mulazzani M. “(1; 1)-knots via the mapping class group of the twice punctured torus,” Adv. Geom. (2004) (to appear).

  14. Norwood F. H., “Every two-generator knot is prime,” Math. Soc., 86, 143-147 (1982).

    Google Scholar 

  15. Mulazzani M., “Cyclic presentations of groups and cyclic branched coverings of (1; 1)-knots,” Bull. Korean Math. Soc., 40, 101-108 (2003).

    Google Scholar 

  16. Cattabriga A. and Mulazzani M. All Strongly-Cyclic Branched Coverings of (1; 1)-Knots Are Dunwoody Manifolds [Preprint] (2003).

Download references

Author information

Authors and Affiliations

  1. Erzurum, Turkey

    H. Aydin & I. Gultekyn

  2. University of Bologna, Italy

    M. Mulazzani

Authors
  1. H. Aydin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. I. Gultekyn
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Mulazzani
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Aydin, H., Gultekyn, I. & Mulazzani, M. Torus Knots and Dunwoody Manifolds. Siberian Mathematical Journal 45, 1–6 (2004). https://doi.org/10.1023/B:SIMJ.0000013008.25556.29

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:SIMJ.0000013008.25556.29

Search

Navigation