Ends of complexes
Hughes, Bruce
Ends of complexes - Cambridge: Cambridge University Press, 2008. - xxv, 353p.; pbk; 24cm. - Cambridge tracts in mathematics, no. 123 .
Includes index and references
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.
https://www.cambridge.org/in/academic/subjects/mathematics/geometry-and-topology/ends-complexes?format=HB&isbn=9780521576253
9780521055192
Complexes
Manifolds--Mathematics
Homotopy
Cellular homology
Geometric relaxation
514.223 / HUG
Ends of complexes - Cambridge: Cambridge University Press, 2008. - xxv, 353p.; pbk; 24cm. - Cambridge tracts in mathematics, no. 123 .
Includes index and references
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.
https://www.cambridge.org/in/academic/subjects/mathematics/geometry-and-topology/ends-complexes?format=HB&isbn=9780521576253
9780521055192
Complexes
Manifolds--Mathematics
Homotopy
Cellular homology
Geometric relaxation
514.223 / HUG
