Geodesic
Samelson Products In Spaces of Self-Homotopy Equivalences
Canadian journal of mathematics, Tome 42 (1990) no. 1, pp. 95-108

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

The homotopy groups of any group-like space are equipped with a Samelson product satisfying, up to sign, the identities of a graded Lie bracket. We shall compute the Samelson product in two kinds of spaces of selfhomotopy equivalences arising when adding a homotopy or a homology group to a space.First, let A→ X be a cofibration with a Moore space M(G,n) as cofibre. For the monoid autA (X) of maps under A homotopic (rel. A) to the identity, the Samelson product is a pairingπn+i(G;X)⨂πn+j(G;X) → π n+i+j(G;X)of homotopy groups with coefficients [1] in G. Theorem 2.1 computes this pairing in terms of a homomorphism associated to a α ∈ πi(autAX)). 
Møller, Jesper Michael. Samelson Products In Spaces of Self-Homotopy Equivalences. Canadian journal of mathematics, Tome 42 (1990) no. 1, pp. 95-108. doi: 10.4153/CJM-1990-006-7
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