The Novikov conjecture : geometry and algebra
Author(s)
Bibliographic Information
The Novikov conjecture : geometry and algebra
（Oberwolfach seminars, v. 33）
Birkhäuser Verlag, c2005
Available at / 31 libraries
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
DC22:516.07/K8712080019297
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Note
Includes bibliographical references (p. [237]-254) and index
Description and Table of Contents
Description
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.
Table of Contents
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.- Poincare 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.
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