Bounding the stable genera of Heegaard splittings from below

Details Bounding the stable genera of Heegaard splittings from below Bounding the stable genera of Heegaard splittings from below

2008-07-17

arxiv.org/abs/0807.2866v1

Mathematics

Geometric Topology

24 pages, 3 figures

Scientific paper

We describe for each postive integer $k$ a 3-manifold with Heegaard surfaces
of genus $2k$ and $2k-1$ such that any common stabilization of these two
surfaces has genus at least $3k-1$. We also show that for every positive $n$,
there is a 3-manifold that has $n$ pairwise non-isotopic Heegaard splittings of
the same genus all of which are stabilized.

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