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

Valdez-Sánchez, Luis

doi:10.2140/agt.2019.19.2151

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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

DOI: 10.2140/agt.2019.19.2151

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

Mathematical Subject Classification 2010

Primary: 57M25

Secondary: 57N10

References

Publication

Received: 14 August 2017

Revised: 6 July 2018

Accepted: 22 August 2018

Published: 20 October 2019

Authors

Luis G Valdez-Sánchez
Department of Mathematical Sciences University of Texas at El Paso El Paso, TX United States

Volume 19, issue 5 (2019)