Thin position and essential planar surfaces
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- by Ying-Qing Wu PDF
- Proc. Amer. Math. Soc. 132 (2004), 3417-3421 Request permission
Abstract:
Abby Thompson proved that if a link $K$ is in thin position but not in bridge position, then the knot complement contains an essential meridional planar surface, and she asked whether some thin level surface must be essential. This note is to give a positive answer to this question, showing that if a link is in thin position but not bridge position, then a thinnest level surface is essential. A theorem of Rieck and Sedgwick follows as a consequence, which says that thin position of a connected sum of small knots comes in the obvious way.References
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Additional Information
- Ying-Qing Wu
- Affiliation: Department of Mathematics, University of Iowa, Iowa City, Iowa 52242
- Email: wu@math.uiowa.edu
- Received by editor(s): February 27, 2003
- Received by editor(s) in revised form: June 16, 2003
- Published electronically: June 17, 2004
- Additional Notes: Partially supported by NSF grant #DMS 0203394
- Communicated by: Ronald A. Fintushel
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 3417-3421
- MSC (2000): Primary 57M25
- DOI: https://doi.org/10.1090/S0002-9939-04-07416-7
- MathSciNet review: 2073319