Algebraic and Geometric Surgery

Erscheinungsjahr 2002
ISBN: 978-0-19-850924-0
Verlag: Oxford University Press

Buch, Englisch, 386 Seiten, Format (B × H): 162 mm x 242 mm, Gewicht: 672 g

This book is an introduction to surgery theory: the standard classification method for high-dimensional manifolds. It is aimed at graduate students who have already had a basic topology course, and would now like to understand the topology of high-dimensional manifolds. This text contains entry-level accounts of the various prerequisites of both algebra and topology, including basic homotopy and homology, Poincare duality, bundles, cobordism, embeddings, immersions, Whitehead torsion, Poincare complexes, spherical fibrations and quadratic forms and formations. While concentrating on the basic mechanics of surgery, this book includes many worked examples, useful drawings for illustration of the algebra and references for further reading.

Autoren/Hrsg.

Ranicki, Andrew

Fachgebiete

• Mathematik | Informatik Mathematik Topologie Analytische Topologie
• Mathematik | Informatik Mathematik Algebra Homologische Algebra
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie

Inhaltsverzeichnis

- Preface

- 1: The surgery classification of manifolds

- 2: Manifolds

- 3: Homotopy and homology

- 4: Poincaré duality

- 5: Bundles

- 6: Cobordism theory

- 7: Embeddings, immersions and singularities

- 8: Whitehead torsion

- 9: Poincaré complexes and spherical fibrations

- 10: Surgery on maps

- 11: The even-dimensional surgery obstruction

- 12: The odd-dimensional surgery obstruction

- 13: The structure set

- References

- Index