Limit search to available items
Book Cover
E-book
Author Nazaĭkinskiĭ, V. E.

Title Elliptic theory and noncommutative geometry : nonlocal elliptic operators / Vladimir E. Nazaikinskii, Anton Yu. Savin, Boris Yu. Sternin
Published Basel ; Boston : Birkhäuser, ©2008

Copies

Description 1 online resource (xii, 224 pages) : illustrations
Series Operator theory, advances and applications ; v. 183. Advances in partial differential equations
Operator theory, advances and applications ; v. 183.
Operator theory, advances and applications. Advances in partial differential equations.
Contents Introduction; Nonlocal Functions and Bundles; Nonlocal Elliptic Operators; Elliptic Operators over C *-Algebras; 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; Index Formula on the Noncommutative Torus; An Application of Higher Traces; Index Formula for a Finite Group
Summary The book deals with nonlocal elliptic differential operators. These are operators whose coefficients involve shifts generated by diffeomorphisms of the manifold on which the operators are defined. The main goal of the study is to relate analytical invariants (in particular, the index) of such operators to topological invariants of the manifold itself. This problem can be solved by modern methods of noncommutative geometry. To make the book self-contained, the authors have included necessary geometric material (C*-algebras and their K-theory, cyclic homology, etc.)
Bibliography Includes bibliographical references (pages 217-221) and index
Notes Print version record
Subject Elliptic operators.
Noncommutative differential geometry.
MATHEMATICS -- Functional Analysis.
Elliptic operators
Noncommutative differential geometry
Form Electronic book
Author Savin, Anton Yu.
Sternin, B. I︠U︡.
ISBN 9783764387754
3764387750