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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