Algebraic Homotopy
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The author describes new tools for the homotopy classification problems, particularly for the classification of homotopy types and for the computation of the group of homotopy equivalences. Applications and examples of such computations are given.Table of contents:Preface; Introduction; List of symbols; 1. Axioms for homotopy theory and examples of cofibration categories; 2. Homotopy theory in a cofibration category; 3. The homotopy spectral sequences in a cofibration category; 4. Extensions, coverings, and cohomology groups of a category; 5. Maps between mapping cones; 6. Homotopy theory of C...
The author describes new tools for the homotopy classification problems, particularly for the classification of homotopy types and for the computation of the group of homotopy equivalences. Applications and examples of such computations are given.
Table of contents:
Preface; Introduction; List of symbols; 1. Axioms for homotopy theory and examples of cofibration categories; 2. Homotopy theory in a cofibration category; 3. The homotopy spectral sequences in a cofibration category; 4. Extensions, coverings, and cohomology groups of a category; 5. Maps between mapping cones; 6. Homotopy theory of CW-complexes; 7. Homotopy theory of complexes in a cofibration category; 8. Homotopy theory of Postnikov towers and the Sullivan-de Rham equivalence of rational homotopy categories; 9. Homotopy theory of reduced complexes; Bibliography; Index.
The author describes new tools for the homotopy classification problems, particularly for the classification of homotopy types and for the computation of the group of homotopy equivalences. Applications and examples of such computations are given.
The author describes new tools for the homotopy classification problems, particularly for the classification of homotopy types and for the computation of the group of homotopy equivalences.
Table of contents:
Preface; Introduction; List of symbols; 1. Axioms for homotopy theory and examples of cofibration categories; 2. Homotopy theory in a cofibration category; 3. The homotopy spectral sequences in a cofibration category; 4. Extensions, coverings, and cohomology groups of a category; 5. Maps between mapping cones; 6. Homotopy theory of CW-complexes; 7. Homotopy theory of complexes in a cofibration category; 8. Homotopy theory of Postnikov towers and the Sullivan-de Rham equivalence of rational homotopy categories; 9. Homotopy theory of reduced complexes; Bibliography; Index.
The author describes new tools for the homotopy classification problems, particularly for the classification of homotopy types and for the computation of the group of homotopy equivalences. Applications and examples of such computations are given.
The author describes new tools for the homotopy classification problems, particularly for the classification of homotopy types and for the computation of the group of homotopy equivalences.
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