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 . Suppose *g*, *h*, and *f* are three homology classes of carried by a single face of the *x*-unit sphere in . 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.

**[S]**B. D. Sterba-Boatwright,*Thurston norm and taut branched surfaces*, Proc. Amer. Math. Soc.**102**(1988), no. 4, 1052–1056. MR**934889**, 10.1090/S0002-9939-1988-0934889-9**[T]**William P. Thurston,*A norm for the homology of 3-manifolds*, Mem. Amer. Math. Soc.**59**(1986), no. 339, i–vi and 99–130. MR**823443****[O]**Ulrich Oertel,*Homology branched surfaces: Thurston’s norm on 𝐻₂(𝑀³)*, Low-dimensional topology and Kleinian groups (Coventry/Durham, 1984), London Math. Soc. Lecture Note Ser., vol. 112, Cambridge Univ. Press, Cambridge, 1986, pp. 253–272. MR**903869****[M]**Lee Mosher,*Surfaces and branched surfaces transverse to pseudo-Anosov flows on 3-manifolds*, J. Differential Geom.**34**(1991), no. 1, 1–36. MR**1114450**

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1994-1246537-4

Article copyright:
© Copyright 1994
American Mathematical Society