Bulletin of the
Korean Mathematical Society BKMS

We study Samelson products on models of function spaces. Given a map $f:X\longrightarrow Y$ between $1$-connected spaces and its Quillen model $\mathbb {L}(f):\mathbb L(V)\longrightarrow \mathbb L(W)$, there is an isomorphism of graded vector spaces $\Theta:H_*(\mathrm{Hom}_{TV}(TV\otimes(\mathbb Q\oplus sV),\mathbb L(W)))\longrightarrow H_*(\mathbb L(W)\oplus\mathrm{Der}(\mathbb L(V),\mathbb L(W)))$. We define a Samelson product on $H_*(\mathrm{Hom}_{TV}(TV\otimes(\mathbb Q\oplus sV),\mathbb L(W)))$.

Keywords: Lie model, Lie algebra of derivations, Samelson product

MSC numbers: 55P62, 55Q15