Heegaard splittings and open books

Jesse Johnson

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arXiv · 1110.2142

Heegaard splittings and open books

Jesse Johnson

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Abstract

We show that if the monodromy of an open book decomposition has sufficiently high displacement distance, acting on the loop and arc complex for a page, then it is the unique minimal Euler characteristic open book for the manifold. In particular, we show that such an open book induces the unique (up to isotopy) minimal genus Heegaard surface for the manifold, and that this Heegaard surface has cyclic mapping class group.

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Jesse Johnson. 2011-10-10. Heegaard splittings and open books. https://arxiv.org/abs/1110.2142

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