Samelson products in function spaces
Bull. Korean Math. Soc. 2015 Vol. 52, No. 4, 1297-1303
Printed July 31, 2015
Jean-Baptiste Gatsinzi and Rugare Kwashira
University of Namibia, University of the Witwatersrand
Abstract : 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
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