#### Volume 19, issue 5 (2019)

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Seifert surfaces for genus one hyperbolic knots in the $3$–sphere

### Luis G Valdez-Sánchez

Algebraic & Geometric Topology 19 (2019) 2151–2231
##### Abstract

We prove that any collection of mutually disjoint and nonparallel genus one orientable Seifert surfaces in the exterior of a hyperbolic knot in the $3$–sphere has at most $5$ components and that this bound is optimal.

##### Keywords
hyperbolic knot, genus one knot, Seifert surface
Primary: 57M25
Secondary: 57N10