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.
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| Series: | Springer monographs in mathematics.
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| Online Access: | Connect to the full text of this electronic book |
Table of Contents:
- I Coherent Homotopy: Coherent mappings
- Coherent homotopy
- Coherent homotopy of sequences
- Coherent homotopy and localization
- Coherent homotopy as a Kleisli category
- II Strong Shape: Resolutions
- Strong expansions
- Strong shape
- Strong shape of metric compacta
- Selected results on strong shape
- III Derived Limits: The derived functors of lim
- lim n and the extension functors Ext n
- The vanishing theorems
- The cofinality theorem
- Higher limits on the category pro-Mod
- IV Homology Groups: Homology pro-groups
- Strong homology groups of height r
- Strong homology as a functor of CH (pro-Top)
- Strong homology of spaces
- Spectral sequences
- Abelian groups
- Strong homology of compact spaces
- Generalized strong homology.