Novikov Conjecture

Geometry and Algebra

AvMatthias Kreck,Wolfgang Lück

Häftad, Engelska, 2004

Del i serien Oberwolfach Seminars

428 kr

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2004-11-22
Mått:178 x 254 x 16 mm
Vikt:547 g
Format:Häftad
Språk:Engelska
Serie:Oberwolfach Seminars
Antal sidor:266
Upplaga:2005
Förlag:Birkhauser Verlag AG
ISBN:9783764371418

Utforska kategorier

Matematik inom Naturvetenskap och teknik

Recensioner i media

From the reviews: This very readable book provides an excellent introduction to the circle of ideas related to the Novikov conjecture. Monatshefte fur 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)

Innehållsförteckning

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.