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Thin position and planar surfaces for graphs in the 3-sphere
Author(s):
Tao
Li
Journal:
Proc. Amer. Math. Soc.
138
(2010),
333-340.
MSC (2000):
Primary 57N10;
Secondary 57M25
Posted:
September 1, 2009
MathSciNet review:
2550199
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References |
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Abstract:
We show that given a trivalent graph in  , 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
DOI:
10.1090/S0002-9939-09-09878-5
PII:
S 0002-9939(09)09878-5
Received by editor(s):
July 31, 2008
Posted:
September 1, 2009
Additional Notes:
Partially supported by NSF grant DMS-0705285
Communicated by:
Daniel Ruberman
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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