Strong Shape and Homology

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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 with distinct advantages over the latter. Strong homology generalizes Steenrod homology and is an invariant of strong shape. The book gives a detailed account based on approximation of spaces by pol…

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Title Statements

Full title :Strong Shape and Homology / by Sibe Mardešić.

Summary

Edition Statements

Publication Date:2000.

Publication Statements

Publisher(s):Springer Berlin Heidelberg
Place of Publication:Berlin, Heidelberg
Language:eng
Publication Date:2000.

The Physical Object

Description:1 online resource (xii, 489 pages)

Edition Identifiers

ISBN:9783662130643, 3662130645
DOI:10.1007/978-3-662-13064-3
oclc:ocn851380873
LC Classification:QA612-612.8
Dewey Decimal:514.2

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.