Effective Algebraic Topology.

Intro -- Contents -- 1. A Five-Lemma for Calculations in Homological Algebra -- I. The Five-Lemma Algorithm -- II. Spectral Sequences of Filiations -- III. The Spectral Sequence of a Map -- 2. Fibrations with Calculable Homology -- I. Calculating the Base Term -- II. Calculating the Fiber Term -- III. Calculating Homology of Fiber Spaces -- Calculating E[sup(2)]-terms -- IV. Applications -- Loop Complexes, Rational Homotopy Groups -- 3. An Algorithm for Calculating Homotopy Groups -- I. Recalling K(G, 1)-Complexes -- II. Calculating K(G, 1)-Complexes -- III. Calculating Homotopy Groups -- Homotopy Groups of Pairs -- Homology Groups of Iterated Loop Complexes -- IV. The Horn-Filling Procedure -- V. Calculating Homology of Postnikov-Complexes -- 4. The Effective Computability of k-Invariants -- I. Calculating Cohomology Groups -- II. The Fundamental Cocycle Algorithm -- III. Postnikov-Complexes and k-Invariants -- Application to Abelian Group Complexes -- IV. k-Invariants of Simple Fibrations -- V. Equivalence of k-Invariants is Decidable.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.