Genus one fibered knots in 3-manifolds with reducible genus two Heegaard splittings

Nozomu Sekino

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arXiv · 1704.08892

Genus one fibered knots in 3-manifolds with reducible genus two Heegaard splittings

Nozomu Sekino

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Abstract

We give a necessary and sufficient condition for a simple closed curve on the boundary of a genus two handlebody to decompose the handlebody into (torus with one boundary component times [0,1]. We use this condition to decide whether a simple closed curve on a genus two Heegaard surface is a GOF-knot (genus one fibered knot) which induces the Heegaard splitting. By using this, we determine the number and the positions with respect to the Heegaard splittings of GOF-knots in the 3-manifolds with reducible genus two Heegaard splittings. This is another proof of results of Morimoto and Baker.

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Nozomu Sekino. 2017-04-28. Genus one fibered knots in 3-manifolds with reducible genus two Heegaard splittings. https://arxiv.org/abs/1704.08892

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