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
Summary
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
Bibliography
Includes bibliographical references (pages 237-254) and index
