Flipping and Stabilizing Heegaard Splittings
نویسنده
چکیده
We show that the number of stabilizations needed to interchange the handlebodies of a Heegaard splitting of a closed 3manifold 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
منابع مشابه
1 8 Ja n 20 01 Heegaard splittings of exteriors of two bridge knots
By H.Goda, M.Scharlemann, and A.Thompson [6] (see also K.Morimoto’s paper [15]), or [13], it is shown that, for each non-trivial two bridge knot K, every genus two Heegaard splitting of E(K) is isotopic to either one of six typical Heegaard splittings (see Figure 7.1). We note that Y.Hagiwara [7] proved that genus three Heegaard splittings obtained by stabilizing the six Heegaard splittings are...
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