Skip to content
Register Sign in Wishlist
Look Inside Variations on a Theme of Borel
eBook forthcoming

Variations on a Theme of Borel
An Essay on the Role of the Fundamental Group in Rigidity

$125.00 (C)

Part of Cambridge Tracts in Mathematics

  • Date Published: December 2022
  • availability: Available
  • format: Hardback
  • isbn: 9781107142596

$ 125.00 (C)
Hardback

Add to cart Add to wishlist

Other available formats:
eBook


Looking for an examination copy?

This title is not currently available for examination. However, if you are interested in the title for your course we can consider offering an examination copy. To register your interest please contact collegesales@cambridge.org providing details of the course you are teaching.

Description
Product filter button
Description
Contents
Resources
Courses
About the Authors
  • In the middle of the last century, after hearing a talk of Mostow on one of his rigidity theorems, Borel conjectured in a letter to Serre a purely topological version of rigidity for aspherical manifolds (i.e. manifolds with contractible universal covers). The Borel conjecture is now one of the central problems of topology with many implications for manifolds that need not be aspherical. Since then, the theory of rigidity has vastly expanded in both precision and scope. This book rethinks the implications of accepting his heuristic as a source of ideas. Doing so leads to many variants of the original conjecture - some true, some false, and some that remain conjectural. The author explores this collection of ideas, following them where they lead whether into rigidity theory in its differential geometric and representation theoretic forms, or geometric group theory, metric geometry, global analysis, algebraic geometry, K-theory, or controlled topology.

    • Introduces tools from a variety of fields, useful to students and researchers in topology, geometry, operator theory, and geometric group theory
    • Uses both true and false variations on the conjecture, to gain a deeper understanding of it
    • Makes much more concrete an area where recent work has been expressed very abstractly
    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

    • Date Published: December 2022
    • format: Hardback
    • isbn: 9781107142596
    • length: 351 pages
    • dimensions: 235 x 158 x 26 mm
    • weight: 0.7kg
    • availability: Available
  • Table of Contents

    1. Introduction
    2. Examples of aspherical manifolds
    3. First contact – The proper category
    4. How can it be true?
    5. Playing the Novikov game
    6. Equivariant Borel conjecture
    7. Existential problems
    8. Epilogue – A survey of some techniques
    References
    Index.

  • Author

    Shmuel Weinberger, University of Chicago
    Shmuel Weinberger is Andrew MacLeish Professor of Mathematics at the University of Chicago. His work is on geometry and topology and their applications. To Weinberger, the only thing cooler than discovering some new geometric result (by any method from any area of mathematics) is discovering a hidden geometric side to the seemingly 'ungeometric'. He has written two other books, one on stratified spaces, and the other on the large-scale structure of spaces of Riemannian metrics using tools from logic. An inaugural Fellow of the American Mathematical Society, he is also a Fellow of the American Academy for the Advancement of Science.

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 ×
warning icon

Turn stock notifications on?

You must be signed in to your Cambridge account to turn product stock notifications on or off.

Sign in Create a Cambridge account arrow icon
×

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.
×