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The ends of a topological space are the directions in which it becomes non-compact by tending to infinity. The tame ends of manifolds are particularly interesting, both for their own sake, and for their use in the classification of high-dimensional compact manifolds. The book is devoted to the related theory and practice of ends, dealing with manifolds and CW complexes in topology and chain complexes in algebra. The first part develops a homotopy model of the behaviour at infinity of a non-compact space. The second part studies tame ends in topology. Tame ends are shown to have a uniform structure, with a periodic shift map. Approximate fibrations are used to prove that tame manifold ends are the infinite cyclic covers of compact manifolds. The third part translates these topological considerations into an appropriate algebraic context, relating tameness to homological properties and algebraic K- and L-theory.

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Book Details

ISBN: 9780521576253
ISBN-10: 0521576253
Format: Hardback
(228mm x 152mm x 25mm)
Pages: 380
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 28-Aug-1996
Country of Publication: United Kingdom

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Books By Author Bruce Hughes

Ends of Complexes by Bruce Hughes

Ends of Complexes

Paperback, January 2008