Sibe Mardesic

Strong Shape and Homology

• Broschiertes Buch

Produktbeschreibung

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.

Produktdetails

• Springer Monographs in Mathematics
• Verlag: Springer / Springer Berlin Heidelberg / Springer, Berlin
• Artikelnr. des Verlages: 978-3-642-08546-8
• Softcover reprint of hardcover 1st ed. 2000
• Seitenzahl: 504
• Erscheinungstermin: 15. Dezember 2010
• Englisch
• Abmessung: 235mm x 155mm x 28mm
• Gewicht: 756g
• ISBN-13: 9783642085468
• ISBN-10: 3642085466
• Artikelnr.: 32079408

Inhaltsangabe

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.