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

References in corpus (4)

• Heegaard splittings and open books
• One-sided and two-sided Heegaard splittings
• The geometry of the disk complex
• Critical Heegaard surfaces obtained by amalgamation

Cited by in corpus (1)

• Disk complexes and genus two Heegaard splittings for non-prime 3-manifolds