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

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.

General

Imprint:	Cambridge UniversityPress
Country of origin:	United Kingdom
Series:	Cambridge Tracts in Mathematics
Release date:	November 2022
Authors:	Shmuel Weinberger
Dimensions:	229 x 152 x 24mm (L x W x T)
Format:	Hardcover
Pages:	351
ISBN-13:	978-1-107-14259-6
Categories:	Books > Science & Mathematics > Mathematics > Algebra > Groups & group theory Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Functional analysis Books > Science & Mathematics > Mathematics > Geometry > Algebraic geometry Books > Science & Mathematics > Mathematics > Topology > General
LSN:	1-107-14259-8
Barcode:	9781107142596

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