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Cover: 9783764371418 | The Novikov Conjecture | Geometry and Algebra | Wolfgang Lück (u. a.)
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The Novikov Conjecture
Geometry and Algebra
Taschenbuch von Wolfgang Lück (u. a.)
Sprache: Englisch

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Beschreibung
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.
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.
Zusammenfassung

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. 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.
Details
Erscheinungsjahr: 2004
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Oberwolfach Seminars
Inhalt: xv
266 S.
ISBN-13: 9783764371418
ISBN-10: 3764371412
Sprache: Englisch
Herstellernummer: 11012870
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Lück, Wolfgang
Kreck, Matthias
Hersteller: Birkhäuser Basel
Springer Basel AG
Oberwolfach Seminars
Maße: 254 x 178 x 16 mm
Von/Mit: Wolfgang Lück (u. a.)
Erscheinungsdatum: 22.11.2004
Gewicht: 0,547 kg
Artikel-ID: 102437337
Zusammenfassung

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. 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.
Details
Erscheinungsjahr: 2004
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Oberwolfach Seminars
Inhalt: xv
266 S.
ISBN-13: 9783764371418
ISBN-10: 3764371412
Sprache: Englisch
Herstellernummer: 11012870
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Lück, Wolfgang
Kreck, Matthias
Hersteller: Birkhäuser Basel
Springer Basel AG
Oberwolfach Seminars
Maße: 254 x 178 x 16 mm
Von/Mit: Wolfgang Lück (u. a.)
Erscheinungsdatum: 22.11.2004
Gewicht: 0,547 kg
Artikel-ID: 102437337
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