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VersandkostenfreiThese 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. Finally, the most recent developments concerning these conjectures are surveyed, including a detailed status report.
The prerequisites consist of a solid knowledge of the basics about manifolds, vector bundles, (co-) homology and characteristic classes.
Inhaltsverzeichnis
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.
Produktdetails
Erscheinungsdatum
22. November 2004
Sprache
englisch
Auflage
2005
Seitenanzahl
288
Reihe
Oberwolfach Seminars
Autor/Autorin
Matthias Kreck, Wolfgang Lück
Illustrationen
XV, 266 p.
Verlag/Hersteller
Produktart
kartoniert
Abbildungen
XV, 266 p.
Gewicht
547 g
Größe (L/B/H)
254/178/16 mm
ISBN
9783764371418
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Pressestimmen
From the reviews:
This very readable book provides an excellent introduction to the circle of ideas related to the Novikov conjecture.
Monatshefte für Mathematik
Overall, the book is very suitable both as an introduction and as a reference, and finds exactly the right balance between detail, comprehensiveness and length of the presentation. It is recommended to everyone with a background in algebraic topology who wants to learn about one or some of the aspects covered. (MATHEMATICAL REVIEWS)
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