Normal all pseudo-Anosov subgroups of mapping class groups

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

Forward citations

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 231 West 18th Avenue Columbus Ohio 43210 USA

Volume 4, issue 1 (2000)

Kim Whittlesey