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

Branched surfaces and Thurston's norm on homology


Authors: Jeffrey L. Tollefson and Ningyi Wang
Journal: Proc. Amer. Math. Soc. 122 (1994), 635-642
MSC: Primary 57M12; Secondary 57N10
MathSciNet review: 1246537
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Abstract: Given a closed, irreducible, orientable 3-manifold M, let x denote the Thurston norm on $ {H_2}(M;R)$. Suppose g, h, and f are three homology classes of $ {H_2}(M;Z)$ carried by a single face of the x-unit sphere in $ {H_2}(M;R)$. In this paper it is shown that there exists a taut, oriented branched surface carrying representatives of g and h and a semi-taut oriented branched surface carrying representatives of all three homology classes.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1246537-4
PII: S 0002-9939(1994)1246537-4
Article copyright: © Copyright 1994 American Mathematical Society