Thin position and planar surfaces for graphs in the 3-sphere
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- Proc. Amer. Math. Soc. 138 (2010), 333-340 Request permission
Abstract:
We show that given a trivalent graph in $S^3$, either the graph complement contains an essential almost meridional planar surface or, after edge slides, thin position for the graph is also bridge position. This can be viewed as an extension of a theorem of Thompson to graphs. It follows that any graph complement always contains a useful planar surface.References
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Additional Information
- Tao Li
- Affiliation: Department of Mathematics, Boston College, Chestnut Hill, Massachusetts 02467
- Email: taoli@bc.edu
- Received by editor(s): July 31, 2008
- Published electronically: September 1, 2009
- Additional Notes: Partially supported by NSF grant DMS-0705285
- Communicated by: Daniel Ruberman
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 333-340
- MSC (2000): Primary 57N10; Secondary 57M25
- DOI: https://doi.org/10.1090/S0002-9939-09-09878-5