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 arethe infinite cyclic covers of compact manifolds. The third part translates these topological considerations into an appropriate algebraic context, relatingtameness to homological properties and algebraic K- and L-theory. INDICE: Introduction; Chapter summaries; Part I. 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; Part II. 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. Homotopytheoretic wrapping up and relaxation; Part III. The Algebraic Theory: 21. Polynomial extensions; 22. Algebraic bands; 23. Algebraic tameness; 24. Relaxation techniques; 25. Algebraic ribbons; 26. Algebraic twist glueing; 27. Wrappingup in algebraic K- and L-theory; Part IV. Appendices; References; Index.
- ISBN: 978-0-521-05519-2
- Editorial: Cambridge University
- Encuadernacion: Rústica
- Páginas: 379
- Fecha Publicación: 20/03/2008
- Nº Volúmenes: 1
- Idioma: Inglés