Matthias Kreck,
Wolfgang Lück
Birkhäuser Basel
2005e druk, 2004
9783764371418
The Novikov Conjecture
Geometry and Algebra
Specificaties
Paperback, 266 blz.
|
Engels
Birkhäuser Basel |
2005e druk, 2004
ISBN13: 9783764371418
Rubricering
Onderdeel van serie
Oberwolfach Seminars
Verwachte levertijd ongeveer 8 werkdagen
Samenvatting
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.
Specificaties
ISBN13:9783764371418
Taal:Engels
Bindwijze:paperback
Aantal pagina's:266
Uitgever:Birkhäuser Basel
Druk:2005
Serie:Oberwolfach Seminars
Inhoudsopgave
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.