Some applications of Gabai's internal hierarchy

Details Some applications of Gabai's internal hierarchy Some applications of Gabai's internal hierarchy

2011-11-03

arxiv.org/abs/1111.0914v1

Mathematics

Geometric Topology

30 pages, 2 figures

Scientific paper

Any Haken 3--manifold (possibly with boundary consisting of tori) can be transformed into a $\mathrm{surface}\times S^1$ by a series of splitting and regluing along incompressible surfaces. This fact was proved by Gabai as an application of his sutured manifold theory. The first half of this paper provides a few technical details in the proof. In the second half of this paper, some applications of Gabai's theorem to Heegaard Floer homology are given. We refine the known results about the Thurson norm and fibrations. We also give some classification results for Floer simple knots in manifolds with positive $b_1$.

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