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Homotopical Nilpotency of Loop-Spaces

Published online by Cambridge University Press:  20 November 2018

C S. Hoo
C S. Hoo*
Affiliation:
University of Alberta, Edmonton, Alberta
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In this paper we shall work in the category of countable CW-complexes with base point and base point preserving maps. All homotopies shall also respect base points. For simplicity, we shall frequently use the same symbol for a map and its homotopy class. Given spaces X, Y, we denote the set of homotopy classes of maps from X to Y by [X, Y]. We have an isomorphism τ: [∑X, Y] → [X, Ω Y] taking each map to its adjoint, where ∑ is the suspension functor and Ω is the loop functor. We shall denote τ(1 ∑x) by e′ and τ-1(1Ωx) by e.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 21 , 1969 , pp. 479 - 484
Copyright
Copyright © Canadian Mathematical Society 1969

References

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