Let Pn(p) be an n-dimensional mod p Moore space and Vn be the mapping cone of an Adams map A:Pn-1(p) → Pn-2p+1(p). This paper gives an unstable splitting of Vm ∧ Vn for a prime p ≥ 5. The proof is based on explicit calculations of [Vn+2p-1,Vn]. As an application, we define a Samelson product on [V*, ΩX] and prove that it satisfies anticommutativity and the Jacobi identity.
Homology, Homotopy and Applications, Vol. 8 (2006), No. 1, pp.169-186.
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