|ISSN 1088-6826(online) ISSN 0002-9939(print)|
Thurston norm and taut branched surfaces
Abstract: Let denote the Thurston norm on , where is a closed, oriented, irreducible, atoroidal three-manifold . U. Oertel defined a taut oriented branched surface to be a branched surface with the property that each surface it carries is incompressible and -minimizing for the (nontrivial) homology class it represents. Given , a face of the -unit sphere in , Oertel then asks: is there a taut oriented branched surface carrying surfaces representing every integral homology class projecting to ? In this article, an example is constructed for which the answer is negative.
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