Geodesic
Homotopical Nilpotency of Loop-Spaces
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 479-484

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Hoo, C S. Homotopical Nilpotency of Loop-Spaces. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 479-484. doi: 10.4153/CJM-1969-053-8
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[1] 1. Berstein, I. and Ganea, T., Homotopical nilpotency, Illinois J. Math. 5 (1961), 99–130. Google Scholar

[2] 2. Ganea, T., Hilton, P. J., and Peterson, F. P., On the homotopy-commutativity of loop-spaces and suspensions, Topology 1 (1962), 133–141. Google Scholar

[3] 3. Hilton, P. J., Nilpotency and U-spaces, Topology 3 (1965), 161–176. Google Scholar

[4] 4. Hoo, C. S., A note on a theorem of Ganea, Hilton and Peterson, Proc. Amer. Math. Soc. 19 (1968), 909–911. Google Scholar

[5] 5. O'Neill, R. C., On U-spaces that are CSN-complexes. I, Illinois J. Math. 8 (1964), 280–290 Google Scholar

[6] 6. Porter, G. J., Higher-order Whitehead products, Topology 3 (1965), 123–135. Google Scholar

[7] 7. Porter, G. J., The homotopy groups of wedges of suspensions, Amer. J. Math. 88 (1966), 655–663. Google Scholar

[8] 8. Stasheff, J., On homotopy abelian H-spaces, Proc. Cambridge Philos. Soc. 57 (1961), 734–745. Google Scholar

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