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

— —

Shmuel Weinberger (University of Chicago)

Variations on a Theme of Borel

An Essay on the Role of the Fundamental Group in Rigidity

Shmuel Weinberger (University of Chicago)

$179.95

Hardback

Not in-store but you can order this
How long will it take?

Availability Information

We source books from suppliers in Australia and overseas. For books we don't currently have in stock, the time it takes to get them from our suppliers can vary widely - from a few days to a few months - so we check each book with each supplier to determine the expected time it will take to be supplied to us.

We then advise you accordingly. If the time taken to get any book is too long for you, you can let us know and we will cancel or adjust your order, and refund as required.

To find out the anticipated arrival time for specific items prior to ordering, please contact us by phone or email:

Phone +61 2 9264 3111, or 1800 4 BOOKS (1800 4 26657) if outside Sydney:
option 1 Abbey's Bookshop (Crime, History, Science, Kids & more) • info@abbeys.com.au
option 2 Language Book Centre (ESL & Foreign Languages) • language@abbeys.com.au
option 3 Galaxy Bookshop (Sci-fi, Fantasy, Romance, Graphic Novels) • sf@galaxybooks.com.au

QTY:

English

Cambridge University Press
08 December 2022

Algebra; Groups & group theory; Functional analysis & transforms; Algebraic geometry; Topology

Series: Cambridge Tracts in Mathematics

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.

By: Shmuel Weinberger (University of Chicago)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Dimensions: Height: 235mm, Width: 158mm, Spine: 26mm
Weight: 700g
ISBN: 9781107142596
ISBN 10: 1107142598
Series: Cambridge Tracts in Mathematics
Pages: 351
Publication Date: 08 December 2022
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

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.

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.