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

Shmuel Weinberger describes here analogies between geometric topology, differential geometry, group theory, global analysis, and noncommutative geometry. He develops deep tools in a setting where they have immediate application. The connections between these fields enrich each and shed light on one another.

List 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.

About the author

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.

Summary

Shmuel Weinberger describes here analogies between geometric topology, differential geometry, group theory, global analysis, and noncommutative geometry. He develops deep tools in a setting where they have immediate application. The connections between these fields enrich each and shed light on one another.

Product details

• Authors: Weinberger Shmuel Weinberger, Shmuel Weinberger, Shmuel (University of Chicago) Weinberger, Weinberger Shmuel
• Publisher: Cambridge University Press ELT
• Languages: English
• Product format: Hardback
• Released: 31.12.2020
• EAN: 9781107142596
• ISBN: 978-1-107-14259-6
• No. of pages: 351
• Series: Cambridge Tracts in Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Miscellaneous; Algebra, MATHEMATICS / Geometry / General, Topology, Algebraic Geometry, Groups & group theory, Functional analysis & transforms, Groups and group theory, Functional analysis and transforms