On nonsimple knots in lens spaces with tunnel number one

Michael J. Williams

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arXiv · 0908.1765

On nonsimple knots in lens spaces with tunnel number one

Michael J. Williams

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Abstract

A knot k in a closed orientable 3-manifold is called nonsimple if the exterior of k possesses a properly embedded essential surface of nonnegative Euler characteristic. We show that if k is a nonsimple prime tunnel number one knot in a lens space M (where M does not contain any embedded Klein bottles), then k is a (1,1) knot. Elements of the proof include handle addition and Dehn filling results/techniques of Jaco, Eudave-Munoz and Gordon as well as structure results of Schultens on the Heegaard splittings of graph manifolds.

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BibTeX RIS

Michael J. Williams. 2009-08-12. On nonsimple knots in lens spaces with tunnel number one. https://arxiv.org/abs/0908.1765

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