The Novikov Conjecture : Geometry and Algebra /
by Matthias Kreck, Wolfgang Lück.
Bok Engelsk 2005
| Medvirkende | Lück, Wolfgang. (author.)
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|---|---|
| Omfang | 1 online resource (279 p.)
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| Utgave | 1st ed. 2005.
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| Opplysninger | Description based upon print version of record.. - A Motivating Problem -- to the Novikov and the Borel Conjecture -- Normal Bordism Groups -- The Signature -- The Signature Theorem and the Novikov Conjecture -- The Projective Class Group and the Whitehead Group -- Whitehead Torsion -- The Statement and Consequences of the s-Cobordism Theorem -- Sketch of the Proof of the s-Cobordism Theorem -- From the Novikov Conjecture to Surgery -- Surgery Below the Middle Dimension I: An Example -- Surgery Below the Middle Dimension II: Systematically -- Surgery in the Middle Dimension I -- Surgery in the Middle Dimension II -- Surgery in the Middle Dimension III -- An Assembly Map -- The Novikov Conjecture for ?n -- Poincaré Duality and Algebraic L-Groups -- Spectra -- Classifying Spaces of Families -- Equivariant Homology Theories and the Meta-Conjecture -- The Farrell-Jones Conjecture -- The Baum-Connes Conjecture -- Relating the Novikov, the Farrell-Jones and the Baum-Connes Conjectures -- Miscellaneous -- Exercises -- Hints to the Solutions of the Exercises.. - 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.
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| Emner | |
| Dewey | |
| ISBN | 3-7643-7315-6
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