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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
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- 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
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
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