Free genus one knots with large volume

Details Free genus one knots with large volume Free genus one knots with large volume

1998-09-24

arxiv.org/abs/math/9809143v1

Mathematics

Geometric Topology

18 pages, including 14 figures

Scientific paper

A Seifert surface F for a knot K is free if the complement of F is a handlebody (i.e., has free fundamental group). The free genus of K is the minimum genus among all free Seifert surfaces for K. In this paper we show that there exist families of hyperbolic knots with arbitrarily large volume, which each have free genus one. This implies that there are knots with free genus one but arbitrarily large canonical genus, and that there exist knots admitting incompressible free Seifert surfaces which cannot be built by applying Seifert's algorithm to a projection of the knot.

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