Commutator Calculus and Groups of Homotopy Classes [Paperback]

In this work the author extends results of rational homotopy theory to a subring of the rationale.A fundamental problem of algebraic topology is the classification of homotopy types and homotopy classes of maps. In this work the author extends results of rational homotopy theory to a subring of the rationale.A fundamental problem of algebraic topology is the classification of homotopy types and homotopy classes of maps. In this work the author extends results of rational homotopy theory to a subring of the rationale.A fundamental problem of algebraic topology is the classification of homotopy types and homotopy classes of maps. In this work the author extends results of rational homotopy theory to a subring of the rationale. The methods of proof employ classical commutator calculus of nilpotent group and Lie algebra theory and rely on an extensive and systematic study of the algebraic properties of the classical homotopy operations (composition and addition of maps, smash products, Whitehead products and higher order James-Hopi invariants). The account is essentially self-contained and should be accessible to non-specialists and graduate students with some background in algebraic topology and homotopy theory.1. Commuter calculus; 2. Distributivity laws in homotopy theory; 3. Homotopy operations on spheres; 4. Higher order Hopf invariants on spheres; 5. The homotopy Lie algebra and the spherical cohomotopy algebra; 6. Groups of homotopy classes; 7. The Hilton-Milnor theorum and its dual.