Higher Index Theory
£64.99
Part of Cambridge Studies in Advanced Mathematics
 Authors:
 Rufus Willett, University of Hawaii, Manoa
 Guoliang Yu, Texas A & M University
 Publication planned for: July 2020
 availability: Not yet published  available from July 2020
 format: Hardback
 isbn: 9781108491068
£
64.99
Hardback
Looking for an inspection copy?
This title is not currently available on inspection

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 Ktheory of operator algebras. This leads to higher index theory, a rapidly developing subject with connections to noncommutative geometry, largescale 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 wellbalanced combination of detailed introductory material (with exercises), cuttingedge developments and references to the wider literature make this a valuable guide to this active area for graduate students and experts alike.
Read more Explains key techniques and motivating background material to introduce a vibrant and highly active area of modern mathematics
 Written in a concrete, examplefocused style, and gives new and simpler approaches in many cases
 A selfcontained reference for many facts that can be difficult to find in the existing literature
Customer reviews
Not yet reviewed
Be the first to review
Review was not posted due to profanity
×Product details
 Publication planned for: July 2020
 format: Hardback
 isbn: 9781108491068
 dimensions: 228 x 152 mm
 contains: 1 b/w illus. 150 exercises
 availability: Not yet published  available from July 2020
Table of Contents
Introduction
Part I. Background:
1. C*algebras
2. Ktheory 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 Khomology
7. Assembly maps and the Baum–Connes conjecture
Part III. Differential Operators:
8. Elliptic operators and Khomology
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.
Sorry, this resource is locked
Please register or sign in to request access. If you are having problems accessing these resources please email lecturers@cambridge.org
Register Sign in» Proceed