Nazaykinskiy / Sternin / Savin | Elliptic Theory and Noncommutative Geometry | Buch | 978-3-7643-8774-7 | sack.de

Buch, Englisch, Band 183, 224 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 530 g

Reihe: Operator Theory: Advances and Applications

Nazaykinskiy / Sternin / Savin

Elliptic Theory and Noncommutative Geometry

Nonlocal Elliptic Operators
2008
ISBN: 978-3-7643-8774-7
Verlag: Springer

Nonlocal Elliptic Operators

Buch, Englisch, Band 183, 224 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 530 g

Reihe: Operator Theory: Advances and Applications

ISBN: 978-3-7643-8774-7
Verlag: Springer


Noncommutative geometry, which can rightfully claim the role of a philosophy in mathematicalstudies,undertakesto replacegoodoldnotionsofclassicalgeometry (suchas manifolds,vectorbundles, metrics, di?erentiable structures,etc. ) by their abstract operator-algebraic analogs and then to study the latter by methods of the theory of operator algebras. At ?rst sight, this pursuit of maximum possible generality harbors the danger of completely forgetting the classical beginnings, so that not only the answers but also the questions would defy stating in traditional terms. Noncommutative geometry itself would become not only a method but also the main subject of investigation according to the capacious but not too practical formula: “Know thyself. ” Fortunately, this is not completely true (or even is completely untrue) in reality: there are numerous problems that are quite classical in their statement (or at least admit an equivalent classical statement) but can be solved only in the framework of noncommutative geometry. One of such problems is the subject of the present book. The classical elliptic theory developed in the well-known work of Atiyah and Singer on the index problem relates an analytic invariant of an elliptic pseud- i?erential operator on a smooth compact manifold, namely, its index, to topol- ical invariants of the manifold itself. The index problem for nonlocal (and hence nonpseudodi?erential) elliptic operators is much more complicated and requires the use of substantially more powerful methods than those used in the classical case.

Nazaykinskiy / Sternin / Savin Elliptic Theory and Noncommutative Geometry jetzt bestellen!

Zielgruppe


Research

Weitere Infos & Material


Analysis of Nonlocal Elliptic Operators.- Nonlocal Functions and Bundles.- Nonlocal Elliptic Operators.- Elliptic Operators over C*-Algebras.- Homotopy Invariants of Nonlocal Elliptic Operators.- Homotopy Classification.- Analytic Invariants.- Bott Periodicity.- Direct Image and Index Formulas in K-Theory.- Chern Character.- Cohomological Index Formula.- Cohomological Formula for the ?-Index.- Index of Nonlocal Operators over C*-Algebras.- Examples.- Index Formula on the Noncommutative Torus.- An Application of Higher Traces.- Index Formula for a Finite Group ?.



Ihre Fragen, Wünsche oder Anmerkungen
Vorname*
Nachname*
Ihre E-Mail-Adresse*
Kundennr.
Ihre Nachricht*
Lediglich mit * gekennzeichnete Felder sind Pflichtfelder.
Wenn Sie die im Kontaktformular eingegebenen Daten durch Klick auf den nachfolgenden Button übersenden, erklären Sie sich damit einverstanden, dass wir Ihr Angaben für die Beantwortung Ihrer Anfrage verwenden. Selbstverständlich werden Ihre Daten vertraulich behandelt und nicht an Dritte weitergegeben. Sie können der Verwendung Ihrer Daten jederzeit widersprechen. Das Datenhandling bei Sack Fachmedien erklären wir Ihnen in unserer Datenschutzerklärung.