Geometry & Topology, Vol. 4 (2000) Paper no. 10, pages 293--307.

Normal all pseudo-Anosov subgroups of mapping class groups

Kim Whittlesey

Abstract. We construct the first known examples of nontrivial, normal, all pseudo-Anosov subgroups of mapping class groups of surfaces. Specifically, we construct such subgroups for the closed genus two surface and for the sphere with five or more punctures. Using the branched covering of the genus two surface over the sphere and results of Birman and Hilden, we prove that a reducible mapping class of the genus two surface projects to a reducible mapping class on the sphere with six punctures. The construction introduces "Brunnian" mapping classes of the sphere, which are analogous to Brunnian links.

Keywords. Mapping class group, pseudo-Anosov, Brunnian

AMS subject classification. Primary: 57M60. Secondary: 20F36, 57N05.

DOI: 10.2140/gt.2000.4.293

E-print: arXiv:math.GT/9906133

Submitted to GT on 24 November 1999. (Revised 28 September 2000.) Paper accepted 3 August 2000. Paper published 10 October 2000.

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Kim Whittlesey
Department of Mathematics, The Ohio State University
231 W 18th Avenue, Columbus, OH 43210, USA

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