Ends of Complexes

Bruce Hughes, Andrew Ranicki (Autoren)

Buch | Softcover

380 Seiten

2008
Cambridge University Press (Verlag)
978-0-521-05519-2 (ISBN)

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The book makes the topology of non-compact spaces accessible to both geometric and algebraic topologists, and algebraists. Recent developments are explained, and tools for further research are provided. In short, this book provides a systematic exposition of the theory and practice of ends of manifolds and CW complexes, along with their algebraic analogues for chain complexes.

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.

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. Homotopy theoretic 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. Wrapping up in algebraic K- and L-theory; Part IV. Appendices; References; Index.

Erscheint lt. Verlag	21.1.2008
Reihe/Serie	Cambridge Tracts in Mathematics
Zusatzinfo	Worked examples or Exercises
Verlagsort	Cambridge
Sprache	englisch
Maße	151 x 228 mm
Gewicht	576 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	0-521-05519-9 / 0521055199
ISBN-13	978-0-521-05519-2 / 9780521055192
Zustand	Neuware