Automorphisms of the three-torus preserving a genus three Heegaard splitting

2007/08/20 by Jesse Johnson, Johnson, Jesse
Mathematics · #57M #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:57M

paper · pdf · doi:10.48550/arxiv.0708.2683

21 pages, 7 figures

arxiv created 2007/08/20 · arxiv updated 2009/12/01

Abstract

The mapping class group of a Heegaard splitting is the group of connected components in the set of automorphisms of the ambient manifold that map the Heegaard surface onto itself. For the genus three Heegaard splitting of the 3-torus, we find an eight element generating set for this group. Six of these generators induce generating elements of the mapping class group of the 3-torus and the remaining two are isotopy trivial in the 3-torus.

Related

• Mapping class groups of Heegaard splittings
• Automorphisms of the 3-sphere that preserve a genus two Heegaard splitting
• Mapping class groups of medium distance Heegaard splittings
• On the disk complexes of weakly reducible, unstabilized Heegaard splittings of genus three III - Generalized Heegaard splittings and mapping classes
• Subgroups of mapping class groups related to Heegaard splittings and bridge decompositions