Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2013; 50(4): 1297-1302

Printed July 1, 2013

https://doi.org/10.4134/BKMS.2013.50.4.1297

Copyright © The Korean Mathematical Society.

Finiteness of mapping class groups

Sungbok Hong and Jin Yang

Korea University, Korea University

Abstract

We prove that the mapping class group of a non-Haken orientable irreducible 3-manifold is finite and we show that the quotient group of the mapping class group by the rotation group is virtually torsion-free if the manifold does not have 2-sphere boundary components.

Keywords: non-Haken manifold, mapping class group, 3-manifold

MSC numbers: Primary 57M99