Mapping class groups of Heegaard splittings of surface bundles

Abstract

Every surface bundle with genus $g$ fiber has a canonical Heegaard splitting of genus $2g+1$. We classify the mapping class groups of such Heegaard splittings in the case when the surface bundle has a sufficiently complicated monodromy map.

6 pages, 1 figure. Minor corrections made in versions 2 and 3