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" Elliptic theory and noncommutative geometry "
Vladimir E. Nazaikinskii, Anton Yu. Savin, Boris Yu. Sternin.
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BL
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| Record Number
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608846
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dltt
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| Main Entry
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Nazaĭkinskiĭ, V. E.
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| Title & Author
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Elliptic theory and noncommutative geometry : nonlocal elliptic operators /\ Vladimir E. Nazaikinskii, Anton Yu. Savin, Boris Yu. Sternin.
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| Publication Statement
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Basel ;Boston :: Birkhäuser,, c2008.
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| Series Statement
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Operator theory, advances and applications ;; v. 183.Advances in partial differential equations.
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| Page. NO
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1 online resource (xii, 224 p.) :: ill.
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| ISBN
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9783764387754 (e-isbn)
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: 3764387750 (e-isbn)
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9783764387747
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3764387742
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| Bibliographies/Indexes
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Includes bibliographical references (p. [217]-221) and index.
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| Contents
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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.
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| Abstract
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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.).
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| Subject
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Elliptic operators.
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Noncommutative differential geometry.
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| Dewey Classification
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515.7242
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| LC Classification
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QA329.42.N396 2008
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| Added Entry
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Savin, Anton Yu.
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Sternin, B. ︠I︡U.
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SpringerLink (Online service)
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