Variations on a Theme of Borel by Shmuel Weinberger - 9781107142596

Variations on a Theme of BorelAn Essay on the Role of the Fundamental Group in Rigidity\nAuthor(s): Shmuel Weinberger\nFormat: Hardback\nPublisher: Cambridge University Press, United Kingdom\nImprint: Cambridge University Press\nISBN-13: 9781107142596, 978-1107142596\nSynopsis\nIn 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 ([url] 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 i.