Once-punctured tori and knots in lens spaces

Abstract

We determine the non-null homologous knots in lens spaces whose exteriors contain properly embedded once-punctured tori. All such knots arise as surgeries on the Whitehead link and are grid number 1 in their lens spaces. As a corollary, we classify once-punctured torus bundles that admit a lens space filling.

37 pages, 29 figures

References in corpus (2)

• Small genus knots in lens spaces have small bridge number
• Combinatorial Description of Knot Floer Homology of Cyclic Branched Covers