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Ends of complexes

Hughes, Bruce.

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Ends of complexes

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Ends of complexes/ Bruce Hughes, Andrew Ranicki.
作者:	Hughes, Bruce.
其他作者:	Ranicki, Andrew,
出版者:	Cambridge :Cambridge University Press, : 1996.,
面頁冊數:	xxv, 353 p. :ill., digital ;24 cm.
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
內容註:	pt. 1. Topology at infinity. 1. End spaces. 2. Limits. 3. Homology at infinity. 4. Cellular homology. 5. Homology of covers. 6. Projective class and torsion. 7. Forward tameness. 8. Reverse tameness. 9. Homotopy at infinity. 10. Projective class at infinity. 11. Infinite torsion. 12. Forward tameness is a homotopy pushout -- pt. 2. Topology over the real line. 13. Infinite cyclic covers. 14. The mapping torus. 15. Geometric ribbons and bands. 16. Approximate fibrations. 17. Geometric wrapping up. 18. Geometric relaxation. 19. Homotopy theoretic twist glueing. 20. Homotopy theoretic wrapping up and relaxation -- pt. 3. The algebraic theory. 21. Polynomial extensions. 22. Algebraic bands. 23. Algebraic tameness. 24. Relaxation techniques. 25. Algebraic ribbons. 26. Algebraic twist glueing. 27. Wrapping up in algebraic K- and L-theory -- pt. 4. Appendices. Appendix A. Locally finite homology with local coefficient. Appendix B.A brief history of end spaces.
標題:	Complexes. -
電子資源:	https://doi.org/10.1017/CBO9780511526299
ISBN:	9780511526299

Ends of complexes
Hughes, Bruce.

Ends of complexes[electronic resource] /Bruce Hughes, Andrew Ranicki. - Cambridge :Cambridge University Press,1996. - xxv, 353 p. :ill., digital ;24 cm. - Cambridge tracts in mathematics ;123. - Cambridge tracts in mathematics ;123..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

pt. 1. Topology at infinity. 1. End spaces. 2. Limits. 3. Homology at infinity. 4. Cellular homology. 5. Homology of covers. 6. Projective class and torsion. 7. Forward tameness. 8. Reverse tameness. 9. Homotopy at infinity. 10. Projective class at infinity. 11. Infinite torsion. 12. Forward tameness is a homotopy pushout -- pt. 2. Topology over the real line. 13. Infinite cyclic covers. 14. The mapping torus. 15. Geometric ribbons and bands. 16. Approximate fibrations. 17. Geometric wrapping up. 18. Geometric relaxation. 19. Homotopy theoretic twist glueing. 20. Homotopy theoretic wrapping up and relaxation -- pt. 3. The algebraic theory. 21. Polynomial extensions. 22. Algebraic bands. 23. Algebraic tameness. 24. Relaxation techniques. 25. Algebraic ribbons. 26. Algebraic twist glueing. 27. Wrapping up in algebraic K- and L-theory -- pt. 4. Appendices. Appendix A. Locally finite homology with local coefficient. Appendix B.A brief history of end spaces.

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.

ISBN: 9780511526299Subjects--Topical Terms:

707345
Complexes.

LC Class. No.: QA608 / .H84 1996

Dewey Class. No.: 514.223

Ends of complexes
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520 $a 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.
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