| Reviews |
| - '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.' - Bulletin Bibliographique
- 'The book is extremely well written and it is very pleasant to read. The definitions and the statements of the results are presented clearly, with a lot of illustrations and judicious examples ... This book is unique on most of the topics that it contains, and, for this and for other reasons, it constitutes a very important contribution to low-dimensional topology literature.' - Anthanase
Papadopoulos, Zentralblatt Math
|
| Description | | - Authored by a leading name in the field
- First book to unify recent developments in this important area
| | This unique reference, aimed at research topologists, gives an exposition of the 'pseudo-Anosov' theory of foliations of 3-manifolds. This theory generalizes Thurston'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 combinatorical objects such as train-tracks, branched surfaces and hierarchies to carry more complicated continuous objects. |
Readership: Graduates and researchers in topology and geometry
| Contents |
Preface
1.
Surface bundles
2.
The topology of S^1
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
|
| Authors, editors,
and contributors |
Danny Calegari, California Institute of Technology
|
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limitation price, format, extent, number of illustrations,
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