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  1. Home
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  3. Commutator Calculus and Groups of Homotopy Classes
  • Cited by 25
Publisher:
Cambridge University Press
Online publication date:
March 2010
Print publication year:
1981
Online ISBN:
9780511662706
DOI:
https://doi.org/10.1017/CBO9780511662706
Subjects:
Mathematics (general), Mathematics, Geometry and Topology, Algebra
Series:
London Mathematical Society Lecture Note Series (50)
Information

Book description

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.

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