Ends of Complexes
Ends of Complexes by Bruce Hughes, published by Cambridge University Press on January 21, 2008, is a comprehensive exploration of the ends of topological spaces, particularly focusing on their noncompact behavior as they approach infinity. This reissue edition spans 380 pages and is presented in English. The book delves into the theory and practice surrounding ends, emphasizing the significance of tame ends in the classification of high-dimensional compact manifolds.
Readers will find a detailed examination of the homotopy model that describes the behavior at infinity of noncompact spaces, alongside an analysis of tame ends in topology. The text illustrates the uniform structure of tame ends and employs approximate fibrations to establish connections between tame manifold ends and infinite cyclic covers of compact manifolds. Additionally, it translates these topological insights into an algebraic framework, linking tameness to homological properties and algebraic K- and L-theory. This book is aimed at researchers engaged in the fields of topology and geometry.
Official synopsis Publisher
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.
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