Vol. 253, No. 1, 2011

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

Jesse Johnson

Vol. 253 (2011), No. 1, 75–94

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.

Heegaard splitting, mapping class group, 3-torus
Mathematical Subject Classification 2000
Primary: 57N10
Received: 28 May 2010
Revised: 13 January 2011
Accepted: 20 January 2011
Published: 28 November 2011
Jesse Johnson
Department of Mathematics
Oklahoma State University
Stillwater OK 74078
United States