Item Details

Geometry of Characteristic Classes

Shigeyuki Morita ; [translated from the Japanese by the author]
Format
Book
Published
Providence, R.I. : American Mathematical Society, c2001.
Language
English
Japanese (translated from)
Uniform Title
Tokuseirui to Kikagaku English
Series
Translations of Mathematical Monographs
Iwanami Series in Modern Mathematics
ISBN
0821821393 (alk. paper)
Contents
  • Chapter 1. De Rham Homotopy Theory 1
  • 1.1. Postnikov decomposition and rational homotopy type 1
  • 1.2. Minimal models of differential graded algebras 18
  • 1.3. Main theorem 34
  • 1.4. Fundamental groups and de Rham homotopy theory 43
  • Chapter 2. Characteristic Classes of Flat Bundles 49
  • 2.1. Flat bundles 49
  • 2.2. Cohomology of Lie algebras 60
  • 2.3. Characteristic classes of flat bundles 66
  • 2.4. Gel'fand-Fuks cohomology 75
  • Chapter 3. Characteristic Classes of Foliations 87
  • 3.1. Foliations 87
  • 3.2. Godbillon-Vey class 91
  • 3.3. Canonical forms on frame bundles of higher orders 100
  • 3.4. Bott vanishing theorem and characteristic classes of foliations 113
  • 3.5. Discontinuous invariants 119
  • 3.6. Characteristic classes of flat bundles II 126
  • Chapter 4. Characteristic Classes of Surface Bundles 135
  • 4.1. Mapping class group and classification of surface bundles 135
  • 4.2. Characteristic classes of surface bundles 144
  • 4.3. Non-triviality of the characteristic classes (1) 151
  • 4.4. Non-triviality of the characteristic classes (2) 160
  • 4.5. Applications of characteristic classes 171
  • Directions and Problems for Future Research 175.
Description
xiii, 185 p. : ill. ; 22 cm.
Notes
Includes bibliographical references (p. 179-182) and index.
Series Statement
Translations of mathematical monographs 0065-9282 ; v. 199
Technical Details
  • Access in Virgo Classic

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    a| Providence, R.I. : b| American Mathematical Society, c| c2001.
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    a| xiii, 185 p. : b| ill. ; c| 22 cm.
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    a| Iwanami series in modern mathematics
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    g| Chapter 1. t| De Rham Homotopy Theory g| 1 -- g| 1.1. t| Postnikov decomposition and rational homotopy type g| 1 -- g| 1.2. t| Minimal models of differential graded algebras g| 18 -- g| 1.3. t| Main theorem g| 34 -- g| 1.4. t| Fundamental groups and de Rham homotopy theory g| 43 -- g| Chapter 2. t| Characteristic Classes of Flat Bundles g| 49 -- g| 2.1. t| Flat bundles g| 49 -- g| 2.2. t| Cohomology of Lie algebras g| 60 -- g| 2.3. t| Characteristic classes of flat bundles g| 66 -- g| 2.4. t| Gel'fand-Fuks cohomology g| 75 -- g| Chapter 3. t| Characteristic Classes of Foliations g| 87 -- g| 3.1. t| Foliations g| 87 -- g| 3.2. t| Godbillon-Vey class g| 91 -- g| 3.3. t| Canonical forms on frame bundles of higher orders g| 100 -- g| 3.4. t| Bott vanishing theorem and characteristic classes of foliations g| 113 -- g| 3.5. t| Discontinuous invariants g| 119 -- g| 3.6. t| Characteristic classes of flat bundles II g| 126 -- g| Chapter 4. t| Characteristic Classes of Surface Bundles g| 135 -- g| 4.1. t| Mapping class group and classification of surface bundles g| 135 -- g| 4.2. t| Characteristic classes of surface bundles g| 144 -- g| 4.3. t| Non-triviality of the characteristic classes (1) g| 151 -- g| 4.4. t| Non-triviality of the characteristic classes (2) g| 160 -- g| 4.5. t| Applications of characteristic classes g| 171 -- t| Directions and Problems for Future Research g| 175.
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