Algebraic and geometric surgery 1st edition by Andrew Ranicki ISBN 0198509243 978-0198509240

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Product details: 

ISBN 10:0198509243

ISBN 13:978-0198509240

Author: Andrew Ranicki

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.

Table of 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 Poincar´e duality 
4.1 Poincar´e duality 
4.2 The homotopy and homology effects of surgery 
4.3 Surfaces 
4.4 Rings with involution 
4.5 Universal Poincar´e 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 Poincar´e complexes and spherical fibrations 
9.1 Geometric Poincar´e 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 odd-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 

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Andrew Ranicki,Algebraic,geometric