Strong Shape and Homology
By: by Sibe Mardešić
Series: Springer Monographs in Mathematics; Springer Monographs in Mathematics
Publisher: Springer Berlin Heidelberg
Published: 2000
Place of publication: Berlin, Heidelberg
Language: eng
Format: [electronic resource] /
Number of pages: 489
ISBN-13: 9783642085468; 9783662130643
Subjects: Mathematics; Algebraic topology; K-theory
Description: 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 polyhedra (ANRs) using the technique of inverse systems. It is intended for researchers and graduate students. Special care is devoted to motivation and bibliographic notes.
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Table of contents: title: I Coherent Homotopy: Coherent mappings; title: Coherent homotopy; title: Coherent homotopy of sequences; title: Coherent homotopy and localization; title: Coherent homotopy as a Kleisli category; title: II Strong Shape: Resolutions; title: Strong expansions; title: Strong shape; title: Strong shape of metric compacta; title: Selected results on strong shape; title: III Derived Limits: The derived functors of lim; title: lim n and the extension functors Ext n; title: The vanishing theorems; title: The cofinality theorem; title: Higher limits on the category pro-Mod; title: IV Homology Groups: Homology pro-groups; title: Strong homology groups of height r; title: Strong homology as a functor of CH (pro-Top); title: Strong homology of spaces; title: Spectral sequences; title: Abelian groups; title: Strong homology of compact spaces; title: Generalized strong homology.