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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Thin position and planar surfaces for graphs in the 3-sphere


Author: Tao Li
Journal: Proc. Amer. Math. Soc. 138 (2010), 333-340
MSC (2000): Primary 57N10; Secondary 57M25
Published electronically: September 1, 2009
MathSciNet review: 2550199
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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.


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Additional Information

Tao Li
Affiliation: Department of Mathematics, Boston College, Chestnut Hill, Massachusetts 02467
Email: taoli@bc.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09878-5
PII: S 0002-9939(09)09878-5
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
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.