Strong Shape and Homology

Sibe Mardesic (Autor)

Buch | Softcover

XII, 489 Seiten

2010
Springer Berlin (Verlag)
978-3-642-08546-8 (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.

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.

Erscheint lt. Verlag	15.12.2010
Reihe/Serie	Springer Monographs in Mathematics
Zusatzinfo	XII, 489 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	754 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	Algebra • algebraic topology • Derived Limit • Homology • Homotopy • homotopy theory • Inverse System • Strong Homology • Strong Shape
ISBN-10	3-642-08546-6 / 3642085466
ISBN-13	978-3-642-08546-8 / 9783642085468
Zustand	Neuware