Bounding canonical genus bounds volume

Mark Brittenham

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arXiv · math/9809142

Bounding canonical genus bounds volume

Mark Brittenham

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Abstract

A Seifert surface for a knot K is called canonical if it can be built by applying Seifert's algorithm to some projection of K. The canonical genus of K is the smallest genus of a surface so obtained. In this paper we show that there is a bound on the volume of a hyperbolic knot which admits a canonical surface of genus g. The bound can, in fact, be chosen to be linear in g.

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Mark Brittenham. 1998-09-24. Bounding canonical genus bounds volume. https://arxiv.org/abs/math/9809142

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