Foliations and the geometry of 3-manifolds

Danny Calegari

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.

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[目次]

  • 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

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この本の情報

書名 Foliations and the geometry of 3-manifolds
著作者等 Calegari, Danny
シリーズ名 Oxford science publications
Oxford mathematical monographs
出版元 Oxford University Press
刊行年月 2007
ページ数 xiv, 363 p.
大きさ 24 cm
ISBN 9780198570080
NCID BA81891603
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言語 英語
出版国 イギリス
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