Skip to content
Register Sign in Wishlist
Higher Index Theory

Higher Index Theory

£64.99

Part of Cambridge Studies in Advanced Mathematics

  • Publication planned for: July 2020
  • availability: Not yet published - available from July 2020
  • format: Hardback
  • isbn: 9781108491068

£ 64.99
Hardback

Pre-order Add to wishlist

Looking for an inspection copy?

This title is not currently available on inspection

Description
Product filter button
Description
Contents
Resources
Courses
About the Authors
  • 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.

    • Explains key techniques and motivating background material to introduce a vibrant and highly active area of modern mathematics
    • Written in a concrete, example-focused style, and gives new and simpler approaches in many cases
    • A self-contained reference for many facts that can be difficult to find in the existing literature
    Read more

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity

    ×

    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?

    ×

    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. 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.

  • Authors

    Rufus Willett, University of Hawaii, Manoa
    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, Texas A & M University
    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.

Sign In

Please sign in to access your account

Cancel

Not already registered? Create an account now. ×

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
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.

Cancel

Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

×
Please fill in the required fields in your feedback submission.
×