Skip to main content
SpringerLink
Log in

Degree of roots of disk twists on 3-dimensional handlebodies

  • Original Paper
  • Published:
Geometriae Dedicata Aims and scope Submit manuscript

Abstract

Margalit and Schleimer (Geom Topol 13(3):1495–1497, 2009) discovered a nontrivial root of the Dehn twist about a nonseparating curve on a closed oriented connected surface. McCullough and Rajeevsarathy (Geom Dedicata 151(1):397–409, 2011) and Monden (Rocky Mt J Math, to appear) obtained the evaluation of the degrees of roots of Dehn twists. In this paper, we discuss existence and degrees of homeomorphisms whose power is equal to disk twist about a nonseparating disk in the mapping class group of the 3-dimensional handlebody.

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

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.

References

  1. Bonahon F.: Cobordism of automorphisms of surfaces. Ann. Sci. Ecole Norm. Sup. (4) 16(2), 237–270 (1983)

    MathSciNet  MATH  Google Scholar 

  2. Luft E.: Actions of the homeotopy group of an orientable 3-dimensional handlebody. Math. Ann. 234, 279–292 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  3. Margalit D., Schleimer S.: Dehn twists have roots. Geom. Topol. 13(3), 1495–1497 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  4. McCullough D., Rajeevsarathy K.: Roots of Dehn twists. Geom. Dedicata 151(1), 397–409 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  5. Monden, N.: On roots of Dehn twists. Rocky Mountain J. Math. (to appear)

  6. Nielsen, J.: Surface Transformation Classes of Algebraically Finite Type. Mat.-fys. Medd. Danske Vid.Selsk. 21 nr.2 (1944) [Collected Math. Papers, vol. 2, Birkhäuser, Boston (1986)]

  7. Rajeevsarathy, K.: Roots of Dehn twists about separating curves. arXiv:1104.0968v1

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Science and Technology, Tokyo University of Science, Noda, Chiba, 278–8510, Japan

    Susumu Hirose

  2. Department of Mathematics, Graduate School of Science, Kyoto University, Kyoto, 606–8502, Japan

    Naoyuki Monden

Authors
  1. Susumu Hirose
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Naoyuki Monden
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Naoyuki Monden.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hirose, S., Monden, N. Degree of roots of disk twists on 3-dimensional handlebodies. Geom Dedicata 164, 73–82 (2013). https://doi.org/10.1007/s10711-012-9759-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10711-012-9759-4

Keywords

Mathematics Subject Classification (2000)

Search

Navigation