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Sommario
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.
Info autore
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.Guoliang Yu is the Powell Chair in Mathematics and University Distinguished Professor at Texas A & M University. He was an invited speaker at the International Congress of Mathematicians in 2006, is a Fellow of the American Mathematical Society and a Simons Fellow in Mathematics. His research interests include large-scale geometry, K-theory, index theory, manifold topology and geometry, and operator algebras.
Riassunto
A friendly introduction to higher index theory, a rapidly-developing subject at the intersection of geometry, topology and operator algebras. A well-balanced combination of introductory material (with exercises), cutting-edge developments and references to the wider literature make this book a valuable guide for graduate students and experts alike.
