Communications in Analysis and Geometry
Volume 19 (2011)
Once-punctured tori and knots in lens spaces
Pages: 347 – 399
We determine the non-null homologous knots in lens spaceswhose exteriors contain properly embedded once-puncturedtori. All such knots arise as surgeries on the Whiteheadlink and are grid number $1$ in their lens spaces. As acorollary, we classify once-punctured torus bundles thatadmit a lens space filling.