Foliations and the Geometry of 3-Manifolds

This unique reference, aimed at research topologists, gives an exposition of the 'pseudo-Anosov' theory of foliations of 3-manifolds. This theory generalizes Thurstone's theory of surface automorphisms and reveals an intimate connection between dynamics, geometry and topology in 3 dimensions. Significant themes returned to throughout the text include the importance of geometry, especially the hyperbolic geometry of surfaces, the importance of monotonicity, especially in 1-dimensional and co-dimensional dynamics, and combinatorial approximation, using finite combonatorical objects such as train-tracks, branched surfaces and hierarchies to carry more complicated continuous objects.

• Preface ; 1. Surface bundles ; 2. The topology of S1 ; 3. Minimal surfaces ; 4. Taut foliations ; 5. Finite depth foliations ; 6. Essential laminations ; 7. Universal circles ; 8. Constructing transverse laminations ; 9. Slitherings and other foliations ; 10. Peano curves ; References ; Index