Bounding canonical genus bounds volume

Details Bounding canonical genus bounds volume Bounding canonical genus bounds volume

1998-09-24

arxiv.org/abs/math/9809142v1

Mathematics

Geometric Topology

9 pages, including 8 figures

Scientific paper

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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