Foliations Transverse to Triangulations of 3-Manifolds

Details Foliations Transverse to Triangulations of 3-Manifolds Foliations Transverse to Triangulations of 3-Manifolds

1998-03-24

arxiv.org/abs/math/9803109v1

Comm. Anal. Geom. 8 (2000), no. 1, 133--158

Mathematics

Geometric Topology

19 pages; This paper has been refereed and will appear in Communications in Analysis and Geometry

Scientific paper

We investigate the combinatorial analogues, in the context of normal surfaces, of taut and transversely measured (codimension 1) foliations of 3-manifolds. We establish that the existence of certain combinatorial structures, a priori weaker than the existence of the corresponding foliation, is sufficient to guarantee that the manifold in question satisfies certain properties, e.g. irreducibility. The finiteness of our combinatorial structures allows us to make our results quantitative in nature and has (coarse) geometrical consequences for the manifold. Furthermore, our techniques give a straightforward combinatorial proof of Novikov's theorem.

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