Strong Shape and Homology

Sibe Mardesic (Autor)

Buch | Hardcover

XII, 489 Seiten

1999 | 2000
Springer Berlin (Verlag)
978-3-540-66198-6 (ISBN)

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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 polyhedra (ANR's) using the technique of inverse systems. It is intended for researchers and graduate students. Special care is devoted to motivation and bibliographic notes.

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
limn and the extension functors Extn
The vanishing theorems
The cofinality theorem
Higher limits on the category pro-Mod
IV Homology Groups: Homology pro-groups
Strong homology groups of height
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

Erscheint lt. Verlag	22.11.1999
Reihe/Serie	Springer Monographs in Mathematics
Zusatzinfo	XII, 489 p.
Verlagsort	Berlin
Sprache	englisch
Maße	156 x 234 mm
Gewicht	850 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	Algebra • algebraic topology • Algebraische Topologie • Derived Limit • Homology • Homotopie • Homotopy • homotopy theory • Inverse System • Strong Homology • Strong Shape
ISBN-10	3-540-66198-0 / 3540661980
ISBN-13	978-3-540-66198-6 / 9783540661986
Zustand	Neuware