Elliptic Theory and Noncommutative Geometry

Nonlocal Elliptic Operators

ISBN: 978-3-7643-8774-7 (Print) 978-3-7643-8775-4 (Online)

Table of contents (15 chapters)

  1. Front Matter

    Pages i-xii

  2. Introduction

    1. No Access

      Chapter

      Pages 1-2

      Introduction

  3. Analysis of Nonlocal Elliptic Operators

    1. Front Matter

      Pages 3-3

    2. No Access

      Chapter

      Pages 5-25

      Nonlocal Functions and Bundles

    3. No Access

      Chapter

      Pages 27-36

      Nonlocal Elliptic Operators

    4. No Access

      Chapter

      Pages 37-55

      Elliptic Operators over C*-Algebras

  4. Homotopy Invariants of Nonlocal Elliptic Operators

    1. Front Matter

      Pages 57-57

    2. No Access

      Chapter

      Pages 59-62

      Homotopy Classification

    3. No Access

      Chapter

      Pages 63-65

      Analytic Invariants

    4. No Access

      Chapter

      Pages 67-74

      Bott Periodicity

    5. No Access

      Chapter

      Pages 75-87

      Direct Image and Index Formulas in K-Theory

    6. No Access

      Chapter

      Pages 89-98

      Chern Character

    7. No Access

      Chapter

      Pages 99-114

      Cohomological Index Formula

    8. No Access

      Chapter

      Pages 115-125

      Cohomological Formula for the Λ-Index

    9. No Access

      Chapter

      Pages 127-136

      Index of Nonlocal Operators over C*-Algebras

  5. Examples

    1. Front Matter

      Pages 137-137

    2. No Access

      Chapter

      Pages 139-143

      Index Formula on the Noncommutative Torus

    3. No Access

      Chapter

      Pages 145-151

      An Application of Higher Traces

    4. No Access

      Chapter

      Pages 153-156

      Index Formula for a Finite Group Г

  6. Back Matter

    Pages 157-224