Rufus Willett, Guoliang Yu

Higher Index Theory (eBook, PDF)

• Format: PDF

Produktbeschreibung

Friendly introduction to higher index theory, a growing subject at the intersection of geometry, topology and operator algebras.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 2. Juli 2020
• Englisch
• ISBN-13: 9781108856911
• Artikelnr.: 70908721

Autorenporträt

Rufus Willett is Professor of Mathematics at the University of Hawaii, Manoa. He has interdisciplinary research interests across large-scale geometry, K-theory, index theory, manifold topology and geometry, and operator algebras.

Inhaltsangabe

Introduction
Part I. Background: 1. C*-algebras
2. K-theory for C*-algebras
3. Motivation: positive scalar curvature on tori
Part II. Roe Algebras, Localisation Algebras, and Assembly: 4. Geometric modules
5. Roe algebras
6. Localisation algebras and K-homology
7. Assembly maps and the Baum-Connes conjecture
Part III. Differential Operators: 8. Elliptic operators and K-homology
9. Products and Poincaré duality
10. Applications to algebra, geometry, and topology
Part IV. Higher Index Theory and Assembly: 11. Almost constant bundles
12. Higher index theory for coarsely embeddable spaces
13. Counterexamples
Appendix A. Topological spaces, group actions, and coarse geometry
Appendix B. Categories of topological spaces and homology theories
Appendix C. Unitary representations
Appendix D. Unbounded operators
Appendix E. Gradings
References
Index of symbols
Subject index.