Strong Shape and Homology
Shape theory is an extension of homotopy theory from the realm of CW-complexes to arbitrary spaces. Besides applications in topology, it has interesting applications in various other areas of mathematics, especially in dynamical systems and C*-algebras. Strong shape is a refinement of ordinary shape...
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| Format: | eBook |
| Language: | English |
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Berlin, Heidelberg
Springer Berlin Heidelberg
2000, 2000
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| Edition: | 1st ed. 2000 |
| Series: | Springer Monographs in Mathematics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- I. Coherent Homotopy
- 1. Coherent mappings
- 2. Coherent homotopy
- 3. Coherent homotopy of sequences
- 4. Coherent homotopy and localization
- 5. Coherent homotopy as a Kleisli category
- II. Strong Shape
- 6. Resolutions
- 7. Strong expansions
- 8. Strong shape
- 9. Strong shape of metric compacta
- 10. Selected results on strong shape
- III. Higher Derived Limits
- 11. The derived functors of lim
- 12. limn and the extension functors Extn
- 13. The vanishing theorems
- 14. The cofinality theorem
- 15. Higher limits on the category pro-Mod
- IV. Homology Groups
- 16. Homology pro-groups
- 17. Strong homology groups of systems
- 18. Strong homology on CH(pro-Top)
- 19. Strong homology of spaces
- 20. Spectral sequences. Abelian groups
- 21. Strong homology of compact spaces
- 22. Generalized strong homology
- References
- List of Special Symbols
- Author Index