Geometry and topology of ℝ-covered foliations

Author:

Calegari Danny

Abstract

An R \mathbb {R} -covered foliation is a special type of taut foliation on a 3 3 -manifold: one for which holonomy is defined for all transversals and all time. The universal cover of a manifold M M with such a foliation can be partially compactified by a cylinder at infinity, somewhat analogous to the sphere at infinity of a hyperbolic manifold. The action of π 1 ( M ) \pi _1(M) on this cylinder decomposes into a product by elements of Homeo ( S 1 ) × Homeo ( R ) \text {Homeo}(S^1)\times \text {Homeo}(\mathbb {R}) . The action on the S 1 S^1 factor of this cylinder is rigid under deformations of the foliation through R \mathbb {R} -covered foliations. Such a foliation admits a pair of transverse genuine laminations whose complementary regions are solid tori with finitely many boundary leaves, which can be blown down to give a transverse regulating pseudo-Anosov flow. These results all fit in an essential way into Thurston’s program to geometrize manifolds admitting taut foliations.

Publisher

American Mathematical Society (AMS)

Subject

General Mathematics

Reference13 articles.

1. dC99 D. Calegari, The geometry of ℝ-covered foliations I, math.GT/9903173.

2. 𝐑-covered foliations of hyperbolic 3-manifolds;Calegari, Danny;Geom. Topol.,1999

3. dC00 D. Calegari, Foliations with one-sided branching, preprint.

4. Uniformization of surface laminations;Candel, Alberto;Ann. Sci. \'{E}cole Norm. Sup. (4),1993

5. Homotopy, isotopy and genuine laminations of 3-manifolds;Gabai, David,1997

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. The geometry of ℝ–covered foliations;Geometry & Topology;2000-12-14

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