The Novikov Conjecture
Geometry and Algebra
(Sprache: Englisch)
These lecture notes contain a guided tour to the Novikov Conjecture and related conjectures due to Baum-Connes, Borel and Farrell-Jones. They begin with basics about higher signatures, Whitehead torsion and the s-Cobordism Theorem. Then an introduction to...
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Klappentext zu „The Novikov Conjecture “
These lecture notes contain a guided tour to the Novikov Conjecture and related conjectures due to Baum-Connes, Borel and Farrell-Jones. They begin with basics about higher signatures, Whitehead torsion and the s-Cobordism Theorem. Then an introduction to surgery theory and a version of the assembly map is presented. Using the solution of the Novikov conjecture for special groups some applications to the classification of low dimensional manifolds are given.
Inhaltsverzeichnis zu „The Novikov Conjecture “
Introduction0. A Motivating Problem
1. Introduction to the Nopvikov and Borel Conjecture
2. Normal Bordism Groups
3. The Signature
4. The Signature Theorem and the Novikov Conjecture
5. The Projective Class Group and the Whitehead Group
6. Whitehead Torsion
7. The Statement and Consequences of the s-Cobordism Theorem
8. Sketch of the Proof of the s-Cobordism Theorem
9. From the Novikov Conjecture to Surgery
10. Surgery Below the Middle Dimension I: An Example
11. Surgery Below the Middle Dimension II: Systematically
12. Surgery in the Middle Dimension I
13. Surgery in the Middle Dimension II
14. Surgery in the Middle Dimension III
15. An Assembly Map
16. The Novikov Conjecture for Z^n
17. Poincaré Duality and Algebraic L-Groups
18. Spectra
19. Classifying Spaces of Families
20. Equivariant Homology Theories and the Meta-Conjecture
21. The Farrell-Jones Conjecture
22. The Baum-Connes Conjecture
23. Relating the Novikov, the Farrell-Jones and the Baum-Connes Conjectures
24. Miscellaneous
25. Exercises
26. Hints to the Solutions of the Exercises
References
Index
Notation
Bibliographische Angaben
- Autoren: Matthias Kreck , Wolfgang Lück
- 2005, 266 Seiten, Maße: 17,8 x 25,4 cm, Kartoniert (TB), Englisch
- Verlag: Springer
- ISBN-10: 3764371412
- ISBN-13: 9783764371418
- Erscheinungsdatum: 22.11.2004
Sprache:
Englisch
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