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.
Notes on file formats
Kim Whittlesey
Department of Mathematics, The Ohio State University
231 W 18th Avenue, Columbus, OH 43210, USA
Email: whittle@math.ohio-state.edu
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