Ends of Complexes (Cambridge Tracts in Mathematics, Series Number 123) - Softcover

Hughes, Bruce; Ranicki, Andrew

Softcover

ISBN 10: 0521055199 ISBN 13: 9780521055192

Publisher: Cambridge University Press, 2008

Synopsis

The ends of a topological space are the directions in which it becomes noncompact 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 behavior at infinity of a noncompact space. The second part studies tame ends in topology. The authors show tame ends to have a uniform structure, with a periodic shift map. They use approximate fibrations 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. This book will appeal to researchers in topology and geometry.

About this title

Book Description

The traditional applications of algebra to topology are to compact spaces. It is now necessary to also understand non-compact topological spaces, especially open manifolds. Hitherto, the relevant material has only been available in research papers (or worse, as folklore). The book makes the topology of non-compact spaces accessible to both geometric and algebraic topologists, and algebraists. Recent developments are explained, and tools for further research are provided. In short, a systematic exposition of the theory and practice of ends of manifolds and CW complexes, along with their algebraic analogues for chain complexes.

Review

'The book gathers together the main strands of the theory of ends of manifolds from the last thirty years and presents a unified and coherent treatment of them. It also contains authoritative expositions of certain topics in topology such as mapping tori and telescopes, often omitted from textbooks. It is thus simultaneously a research monograph and a useful reference.' Proceedings of the Edinburgh Mathematical Society

'This is a highly specialized monograph which is very clearly written and made as accessible for the reader as possible ... It is absolutely indispensable for any specialist in the field.' European Mathematical Society

Edition details

• Publisher: Cambridge University Press
• Publication date: 2008
• Language: English
• ISBN 10: 0521055199
• ISBN 13: 9780521055192
• Binding: Paperback
• Number of pages: 380