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.Read more
- 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
Not yet reviewed
Be the first to review
Review was not posted due to profanity×
- Publication planned for: December 2022
- format: Hardback
- isbn: 9781107142596
- length: 351 pages
- dimensions: 229 x 152 x 24 mm
- weight: 0.636kg
- availability: Available
Table of Contents
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
Sorry, this resource is locked
Please register or sign in to request access. If you are having problems accessing these resources please email firstname.lastname@example.orgRegister Sign in
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 ×
Are you sure you want to delete your account?
This cannot be undone.
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.×