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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