Three-manifolds, Foliations and Circles, I

William P. Thurston

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arXiv · math/9712268

Three-manifolds, Foliations and Circles, I

William P. Thurston

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Abstract

This paper investigates certain foliations of three-manifolds that are hybrids of fibrations over the circle with foliated circle bundles over surfaces: a 3-manifold slithers around the circle when its universal cover fibers over the circle so that deck transformations are bundle automorphisms. Examples include hyperbolic 3-manifolds of every possible homological type. We show that all such foliations admit transverse pseudo-Anosov flows, and that in the universal cover of the hyperbolic cases, the leaves limit to sphere-filling Peano curves. The skew R-covered Anosov foliations of Sergio Fenley are examples. We hope later to use this structure for geometrization of slithered 3-manifolds.

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BibTeX RIS

William P. Thurston. 1997-12-30. Three-manifolds, Foliations and Circles, I. https://arxiv.org/abs/math/9712268

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