Flipping and stabilizing Heegaard splittings

Details Flipping and stabilizing Heegaard splittings Flipping and stabilizing Heegaard splittings

2008-05-28

arxiv.org/abs/0805.4422v1

Mathematics

Geometric Topology

22 pages, 7 figures

Scientific paper

We show that the number of stabilizations needed to interchange the handlebodies of a Heegaard splitting of a closed 3-manifold by an isotopy is bounded below by the smaller of twice its genus or half its Hempel distance. This is a combinatorial version of a proof by Hass, Thompson and Thurston of a similar theorem, but with an explicit bound in terms of distance. We also show that in a 3-manifold with boundary, the stable genus of a Heegaard splitting and a boundary stabilization of itself is bounded below by the same value.

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