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Cover: 9780387942483 | Algebraic K-Theory and Its Applications | Jonathan Rosenberg | Buch
Bild: 9780387942483 | Algebraic K-Theory and Its Applications | Jonathan Rosenberg | Buch
Cover: 9780387942483 | Algebraic K-Theory and Its Applications | Jonathan Rosenberg | Buch
Bild: 9780387942483 | Algebraic K-Theory and Its Applications | Jonathan Rosenberg | Buch
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Algebraic K-Theory and Its Applications
Buch von Jonathan Rosenberg
Sprache: Englisch

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Beschreibung
Algebraic K-Theory plays an important role in many areas of modern mathematics: most notably algebraic topology, number theory, and algebraic geometry, but even including operator theory. The broad range of these topics has tended to give the subject an aura of inapproachability. This book, based on a course at the University of Maryland in the fall of 1990, is intended to enable graduate students or mathematicians working in other areas not only to learn the basics of algebraic K-Theory, but also to get a feel for its many applications. The required prerequisites are only the standard one-year graduate algebra course and the standard introductory graduate course on algebraic and geometric topology. Many topics from algebraic topology, homological algebra, and algebraic number theory are developed as needed. The final chapter gives a concise introduction to cyclic homology and its interrelationship with K-Theory.
Algebraic K-Theory plays an important role in many areas of modern mathematics: most notably algebraic topology, number theory, and algebraic geometry, but even including operator theory. The broad range of these topics has tended to give the subject an aura of inapproachability. This book, based on a course at the University of Maryland in the fall of 1990, is intended to enable graduate students or mathematicians working in other areas not only to learn the basics of algebraic K-Theory, but also to get a feel for its many applications. The required prerequisites are only the standard one-year graduate algebra course and the standard introductory graduate course on algebraic and geometric topology. Many topics from algebraic topology, homological algebra, and algebraic number theory are developed as needed. The final chapter gives a concise introduction to cyclic homology and its interrelationship with K-Theory.
Zusammenfassung
Algebraic K-Theory plays an important role in many areas of mathematics: most notably algebraic topology, number theory, and algebraic geometry, but even including operator theory. This book is intended to enable graduate students or mathematicians working in other areas to learn the basics of algebraic K-Theory and to get a feel for its applications. Exercises are an integral part of the book.
Inhaltsverzeichnis
1. K0 of Rings.- 1. Defining K0.- 2. K0 from idempotents.- 3. K0 of PIDs and local rings.- 4. K0 of Dedekind domains.- 5. Relative K0 and excision.- 6. An application: Swan's Theorem and topological K- theory.- 7. Another application: Euler characteristics and the Wall finiteness obstruction.- 2.K1 of Rings.- 1. Defining K1.- 2. K1 of division rings and local rings.- 3. 1 of PIDs and Dedekind domains.- 4. Whitehead groups and Whitehead torsion.- 5. Relative K1 and the exact sequence.- 3. K0 and K1 of Categories, Negative K-Theory.- 1. K0 and K1 of categories, Go and G1 of rings.- 2. The Grothendieck and Bass-Heller-Swan Theorems.- 3. Negative K-theory.- 4. Milnor's K2.- 1. Universal central extensions and H2.- 2. The Steinberg group.- 3. Milnor's K2.- 4. Applications of K2.- 5. The +?Construction and Quillen K-Theory.- 1. An introduction to classifying spaces.- 2. Quillen's +?construction and its basic properties.- 3. A survey of higher K-theory.- 6. Cyclic homology and its relation to K-Theory.- 1. Basics of cyclic homology.- 2. The Chern character.- 3. Some applications.- References.- Books and Monographs on Related Areas of Algebra, Analysis, Number Theory, and Topology.- Books and Monographs on Algebraic K-Theory.- Specialized References.- Notational Index.
Details
Erscheinungsjahr: 1994
Fachbereich: Arithmetik & Algebra
Genre: Importe, Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Inhalt: x
394 S.
ISBN-13: 9780387942483
ISBN-10: 0387942483
Sprache: Englisch
Einband: Gebunden
Autor: Rosenberg, Jonathan
Hersteller: Springer US
Springer New York
Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße: 241 x 160 x 28 mm
Von/Mit: Jonathan Rosenberg
Erscheinungsdatum: 24.06.1994
Gewicht: 0,776 kg
Artikel-ID: 104859535
Zusammenfassung
Algebraic K-Theory plays an important role in many areas of mathematics: most notably algebraic topology, number theory, and algebraic geometry, but even including operator theory. This book is intended to enable graduate students or mathematicians working in other areas to learn the basics of algebraic K-Theory and to get a feel for its applications. Exercises are an integral part of the book.
Inhaltsverzeichnis
1. K0 of Rings.- 1. Defining K0.- 2. K0 from idempotents.- 3. K0 of PIDs and local rings.- 4. K0 of Dedekind domains.- 5. Relative K0 and excision.- 6. An application: Swan's Theorem and topological K- theory.- 7. Another application: Euler characteristics and the Wall finiteness obstruction.- 2.K1 of Rings.- 1. Defining K1.- 2. K1 of division rings and local rings.- 3. 1 of PIDs and Dedekind domains.- 4. Whitehead groups and Whitehead torsion.- 5. Relative K1 and the exact sequence.- 3. K0 and K1 of Categories, Negative K-Theory.- 1. K0 and K1 of categories, Go and G1 of rings.- 2. The Grothendieck and Bass-Heller-Swan Theorems.- 3. Negative K-theory.- 4. Milnor's K2.- 1. Universal central extensions and H2.- 2. The Steinberg group.- 3. Milnor's K2.- 4. Applications of K2.- 5. The +?Construction and Quillen K-Theory.- 1. An introduction to classifying spaces.- 2. Quillen's +?construction and its basic properties.- 3. A survey of higher K-theory.- 6. Cyclic homology and its relation to K-Theory.- 1. Basics of cyclic homology.- 2. The Chern character.- 3. Some applications.- References.- Books and Monographs on Related Areas of Algebra, Analysis, Number Theory, and Topology.- Books and Monographs on Algebraic K-Theory.- Specialized References.- Notational Index.
Details
Erscheinungsjahr: 1994
Fachbereich: Arithmetik & Algebra
Genre: Importe, Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Inhalt: x
394 S.
ISBN-13: 9780387942483
ISBN-10: 0387942483
Sprache: Englisch
Einband: Gebunden
Autor: Rosenberg, Jonathan
Hersteller: Springer US
Springer New York
Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße: 241 x 160 x 28 mm
Von/Mit: Jonathan Rosenberg
Erscheinungsdatum: 24.06.1994
Gewicht: 0,776 kg
Artikel-ID: 104859535
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