Ends of complexes

By:

Hughes, Bruce

Contributor(s):

Ranicki, Andrew [Co-author]

Series: Cambridge tracts in mathematics, no. 123Publication details: Cambridge University Press, 2008. Cambridge:Description: xxv, 353p.; pbk; 24cmISBN:

9780521055192

Subject(s):

DDC classification:

514.223 HUG

Summary: 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

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Holdings
Item type	Current library	Collection	Call number	Copy number	Status	Date due	Barcode
Books	IIT Gandhinagar	General	514.223 HUG (Browse shelf(Opens below))	Books India	Available		031773

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

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