Thurston Norm

  • Michael Kapovich
Part of the Modern Birkhäuser Classics book series (MBC)


In this chapter, we prove the following theorem. Theorem 2.1 (W. Thurston [Thu85]). Suppose that M is a compact atoroidal orientable 3-manifold such that rank \(H_2 (M, \partial M; Z) \leq 2\). Then M contains an embedded superincompressible surface that is not a fiber in a fibration of M over S 1 and that represents a nontrivial element of \(H_2 (M, \partial M; Z)\). The Proof of this theorem will be finished in Section 2.3. Our proof is essentially the same as Thurston’s.


Euler Characteristic Homology Class Nontrivial Element Integer Coefficient Kernel Distribution 
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Copyright information

© Birkhäuser Boston 2009

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of California, DavisDavisU.S.A.

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