
Higher Index Theory
Cambridge University Press
Published on 2. July 2020
Book
Hardback
592 pages
978-1-108-49106-8 (ISBN)
Description
Index theory studies the solutions to differential equations on geometric spaces, their relation to the underlying geometry and topology, and applications to physics. If the space of solutions is infinite dimensional, it becomes necessary to generalise the classical Fredholm index using tools from the K-theory of operator algebras. This leads to higher index theory, a rapidly developing subject with connections to noncommutative geometry, large-scale geometry, manifold topology and geometry, and operator algebras. Aimed at geometers, topologists and operator algebraists, this book takes a friendly and concrete approach to this exciting theory, focusing on the main conjectures in the area and their applications outside of it. A well-balanced combination of detailed introductory material (with exercises), cutting-edge developments and references to the wider literature make this a valuable guide to this active area for graduate students and experts alike.
Reviews / Votes
'This book is an exceptional blend of clear, concise, delightfully written exposition and thorough scholarship. The book also has much to offer more experienced researchers.' Peter Haskell, European Mathematical SocietyMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Product notice
sewn/stitched
Cloth over boards
Illustrations
Worked examples or Exercises; 1 Halftones, black and white
Dimensions
Height: 231 mm
Width: 155 mm
Thickness: 38 mm
Weight
962 gr
ISBN-13
978-1-108-49106-8 (9781108491068)
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Schweitzer Classification
Other editions
Additional editions

Rufus Willett
Higher Index Theory
E-Book
07/2020
Cambridge University Press
€63.99
Available for download

Rufus Willett | Guoliang Yu
Higher Index Theory
E-Book
06/2020
Cambridge University Press
€84.99
Available for download
Persons
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.
Content
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 Poincare 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.