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arXiv · 0709.2249

Heegaard Splittings of Twisted Torus Knots

Yoav Moriah·Eric Sedgwick
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Abstract

Little is known on the classification of Heegaard splittings for hyperbolic 3-manifolds. Although Kobayashi gave a complete classification of Heegaard splittings for the exteriors of 2-bridge knots, our knowledge of other classes is extremely limited. In particular, there are very few hyperbolic manifolds that are known to have a unique minimal genus splitting. Here we demonstrate that an infinite class of hyperbolic knot exteriors, namely exteriors of certain "twisted torus knots" originally studied by Morimoto, Sakuma and Yokota, have a unique minimal genus Heegaard splitting of genus two. We also conjecture that these manifolds possess irreducible yet weakly reducible splittings of genus three. There are no known examples of such Heegaard splittings.

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BibTeXRIS

Yoav Moriah, Eric Sedgwick. 2008-01-31. Heegaard Splittings of Twisted Torus Knots. https://arxiv.org/abs/0709.2249

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