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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Normal all pseudo-Anosov subgroups of mapping class groups

Kim Whittlesey

Geometry & Topology 4 (2000) 293–307

arXiv: math.GT/9906133

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
Mathematical Subject Classification 2000
Primary: 57M60
Secondary: 20F36, 57N05
References
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Publication
Received: 24 November 1999
Revised: 28 September 2000
Accepted: 3 August 2000
Published: 10 October 2000
Proposed: Joan Birman
Seconded: Shigeyuki Morita, Walter Neumann
Authors
Kim Whittlesey
Department of Mathematics
The Ohio State University
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Columbus
Ohio 43210
USA