A recent result on the mapping class groups
by
Yining Xia
Northern Illinois University

The mapping class group \Gamma_g is defined to be the group of path components of the group of orientation preserving diffeomorphisms of an oriented closed surface S_g of genus g. A basic question concerning \Gamma_g is to understand its subgroup structure. We study an integer invariant p(\Gamma) for an infinite group \Gamma as a local obstruction for a group isomorphic to a subgroup of \Gamma. In particular, we calculate the invariant p(\Gamma_g). As a consequence, we prove that some interesting infinite groups can not be embedded into a mapping class group.

Date received: January 31, 1996

Copyright © 1996 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caaa-36.