Variations on a Theme of Borel
(Book #213 in the Cambridge Tracts in Mathematics Series)
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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.
Format:Hardcover
Language:English
ISBN:1107142598
ISBN13:9781107142596
Release Date:December 2022
Publisher:Cambridge University Press
Length:351 Pages
Weight:1.55 lbs.
Dimensions:0.9" x 6.0" x 9.0"
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