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Tunnel number one, genus one fibered knots

2006/06/15 by Kenneth L. Baker, Baker, Kenneth L., Jesse E. Johnson +3
Mathematics · #57M12 #57M25 (Secondary) #57M50 (Primary) #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:57M12 #msc:57M25 #msc:57M50

paper · pdf · doi:10.48550/arxiv.math/0606379

12 pages, 4 figures; incorporated referee comments; accepted by CAG

arxiv created 2007/02/02 · arxiv updated 2009/12/01

Abstract

We determine the genus one fibered knots in lens spaces that have tunnel number one. We also show that every tunnel number one, once-punctured torus bundle is the result of Dehn filling a component of the Whitehead link in the 3-sphere.

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