Geometriae Dedicata

, Volume 157, Issue 1, pp 217–225 | Cite as

Abelianization and Nielsen realization problem of the mapping class group of a handlebody

  • Susumu Hirose
Original Research


For the oriented 3-dimensional handlebody constructed from a 3-ball by attaching g 1-handles, it is shown that the natural surjection from the group of orientation preserving diffeomorphisms to the mapping class group has no section when g is at least 5. In order to prove the above result, we show the vanishing of the first homology group with the real coefficient of the mapping class group of the handlebody with genus g at least 3 and a distinguished disk on its boundary.


Mapping class group 3-Dimensional handlebody Abelianization Nielsen realization 

Mathematics Subject Classification (2000)

57M60 57N10 


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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of Mathematics, Graduate School of Science and EngineeringSaga UniversitySagaJapan
  2. 2.Department of Mathematics, Faculty of Science and TechnologyTokyo University of ScienceNoda, ChibaJapan

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