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Variations on a Theme of Borel

Variations on a Theme of Borel

An Essay on the Role of the Fundamental Group in Rigidity

Shmuel Weinberger

Cambridge University Press
Publication date : 2022-12-08

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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.

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About the book

Author

Shmuel Weinberger

Imprint

Cambridge University Press

Collection

n.c

Publication date

2022-12-08

Pages

n.c

Print ISBN

9781107142596

Language

English

Ebook informations

EAN PDF

9781108916844

Price

£104.44

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File size 2488 Ko

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About author(s)

Shmuel Weinberger

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