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Geometriae Dedicata

, Volume 164, Issue 1, pp 73–82 | Cite as

Degree of roots of disk twists on 3-dimensional handlebodies

  • Susumu Hirose
  • Naoyuki Monden
Original Paper
  • 99 Downloads

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.

Keywords

Mapping class group 3-Dimensional handlebody Disk twist Root 

Mathematics Subject Classification (2000)

57M99 

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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Science and TechnologyTokyo University of ScienceNodaJapan
  2. 2.Department of Mathematics, Graduate School of ScienceKyoto UniversityKyotoJapan

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