Surgery Theory Foundations /
This monograph provides a comprehensive introduction to surgery theory, the main tool in the classification of manifolds. Surgery theory was developed to carry out the so-called Surgery Program, a basic strategy to decide whether two closed manifolds are homeomorphic or diffeomorphic. This book prov...
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| Hauptverfasser: | , |
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| Körperschaft: | |
| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Cham :
Springer International Publishing : Imprint: Springer,
2024.
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| Ausgabe: | 1st ed. 2024. |
| Schriftenreihe: | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,
362 |
| Schlagworte: | |
| Online-Zugang: | https://doi.org/10.1007/978-3-031-56334-8 |
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Inhaltsangabe:
- 1 Introduction
- 2 The s-Cobordism Theorem
- 3 Whitehead Torsion
- 4 The Surgery Step and ξ-Bordism
- 5 Poincaré Duality
- 6 The Spivak Normal Structure
- 7 Normal Maps and the Surgery Problem
- 8 The Even-Dimensional Surgery Obstruction
- 9 The Odd-Dimensional Surgery Obstruction
- 10 Decorations and the Simple Surgery Obstruction
- 11 The Geometric Surgery Exact Sequence
- 12 Homotopy Spheres
- 13 The Geometric Surgery Obstruction Group and Surgery Obstruction
- 14 Chain Complexes
- 15 Algebraic Surgery
- 16 Brief Survey of Computations of L-Groups
- 17 The Homotopy Type of G/TOP, G/PL, and G/O
- 18 Computations of Topological Structure Sets of some Prominent Closed Manifolds
- 19 Topological Rigidity
- 20 Modified Surgery
- 21 Solutions of the Exercises.