Ends of Complexes

ISBN-13: 9780521576253 / Angielski / Twarda / 1996 / 380 str.

Bruce Hughes; B. Hughes; A. Ranicki

Opis

The ends of a topological space are the directions in which it becomes noncompact 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 behavior at infinity of a noncompact space. The second part studies tame ends in topology. The authors show tame ends to have a uniform structure, with a periodic shift map. They use approximate fibrations 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. This book will appeal to researchers in topology and geometry.

Recenzje

'This is a highly specialized monograph which is very clearly written and made as accessible for the reader as possible … It is absolutely indispensable for any specialist in the field.' European Mathematical Society

Spis treści

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.