Advertisement

Thurston Norm

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

Abstract

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.

Keywords

Euler Characteristic Homology Class Nontrivial Element Integer Coefficient Kernel Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Birkhäuser Boston 2009

Authors and Affiliations

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

Personalised recommendations