Communications in Analysis and Geometry

Volume 19 (2011)

Number 2

Once-punctured tori and knots in lens spaces

Pages: 347 – 399



Kenneth L. Baker (Department of Mathematics, University of Miami)


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.

Published 2 September 2011