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

 

Thurston norm and taut branched surfaces


Author: B. D. Sterba-Boatwright
Journal: Proc. Amer. Math. Soc. 102 (1988), 1052-1056
MSC: Primary 57N10
MathSciNet review: 934889
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Abstract: Let $ x$ denote the Thurston norm on $ {H_2}(N;{\mathbf{R}})$, where $ N$ is a closed, oriented, irreducible, atoroidal three-manifold $ N$. U. Oertel defined a taut oriented branched surface to be a branched surface with the property that each surface it carries is incompressible and $ x$-minimizing for the (nontrivial) homology class it represents. Given $ \varphi $, a face of the $ x$-unit sphere in $ {H_2}(N;{\mathbf{R}})$, Oertel then asks: is there a taut oriented branched surface carrying surfaces representing every integral homology class projecting to $ \varphi $? In this article, an example is constructed for which the answer is negative.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0934889-9
PII: S 0002-9939(1988)0934889-9
Keywords: Branched surface, taut oriented branched surface, Thurston norm, $ x$-minimizing surface
Article copyright: © Copyright 1988 American Mathematical Society