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Algebraic and geometric surgery

Author: Andrew Ranicki; Oxford University Press.
Publisher: Oxford : Clarendon Press ; New York : Oxford University Press, 2002.
Series: Oxford mathematical monographs.; Oxford science publications.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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.
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Ranicki, Andrew, 1948-
Algebraic and geometric surgery.
Oxford : Clarendon Press ; New York : Oxford University Press, 2002
(DLC) 2002075720
(OCoLC)50730719
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Andrew Ranicki; Oxford University Press.
ISBN: 9780191545245 0191545244 9780191708725 0191708720
OCLC Number: 316102707
Description: 1 online resource (xi, 373 pages) : illustrations.
Contents: 1. The surgery classification of manifolds --
2. Manifolds --
2.1. Differentiable manifolds --
2.2. Surgery --
2.3. Morse theory --
2.4. Handles --
3. Homotopy and homology --
3.1. Homotopy --
3.2. Homology --
4. Poincare duality --
4.1. Poincare duality --
4.2. The homotopy and homology effects of surgery --
4.3. Surfaces --
4.4. Rings with involution --
4.5. Universal Poincare duality --
5. Bundles --
5.1. Fibre bundles and fibrations --
5.2. Vector bundles --
5.3. The tangent and normal bundles --
5.4. Surgery and bundles --
5.5. The Hopf invariant and the J-homomorphism --
6. Cobordism theory --
6.1. Cobordism and transversality --
6.2. Framed cobordism --
6.3. Unoriented and oriented cobordism --
6.4. Signature --
7. Embeddings, immersions, and singularities --
7.1. The Whitney Immersion and Embedding Theorems. 7.2. Algebraic and geometric intersections --
7.3. The Whitney trick --
7.4. The Smale-Hirsch classification of immersions --
7.5. Singularities --
8. Whitehead torsion --
8.1. The Whitehead group --
8.2. The h- and s-Cobordism Theorems --
8.3. Lens spaces --
9. Poincare complexes and spherical fibrations --
9.1. Geometric Poincare complexes --
9.2. Spherical fibrations --
9.3. The Spivak normal fibration --
9.4. Browder-Novikov theory --
10. Surgery on maps --
10.1. Surgery on normal maps --
10.2. The regular homotopy groups --
10.3. Kernels --
10.4. Surgery below the middle dimension --
10.5. Finite generation --
11. The even-dimensional surgery obstruction --
11.1. Quadratic forms --
11.2. The kernel form --
11.3. Surgery on forms --
11.4. The even-dimensional L-groups --
11.5. The even-dimensional surgery obstruction. 12. The old-dimensional surgery obstruction --
12.1. Quadratic formations --
12.2. The kernel formation --
12.3. The odd-dimensional L-groups --
12.4. The odd-dimensional surgery obstruction --
12.5. Surgery on formations --
12.6. Linking forms --
13. The structure set --
13.1. The structure set --
13.2. The simple structure set --
13.3. Exotic spheres --
13.4. Surgery obstruction theory.
Series Title: Oxford mathematical monographs.; Oxford science publications.
Responsibility: Andrew Ranicki.
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Abstract:

This book provides an introduction to surgery theory; the standard classification method for high dimension manifolds.  Read more...

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An excellent framework for various courses in Surgery Theory ... very readable ... I read this fine and carefully written book with great pleasure, and highly recommend it for everyone who wants to Read more...

 
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