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

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

2007-08-20

arxiv.org/abs/0708.2683v1

Mathematics

Geometric Topology

21 pages, 7 figures

Scientific paper

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.

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