Once-punctured tori and knots in lens spaces

2006/12/18 by Kenneth L. Baker, Baker, Kenneth L.
Mathematics · #57M27 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:57M27

paper · pdf · doi:10.48550/arxiv.math/0612525

37 pages, 29 figures

arxiv created 2007/05/07 · arxiv updated 2009/12/01

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.

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