Unstable splitting of V(1) ∧ V(1) and its applications

Takahisa Shiina

Let Pⁿ(p) be an n-dimensional mod p Moore space and Vⁿ be the mapping cone of an Adams map A:P^n-1(p) → P^n-2p+1(p). This paper gives an unstable splitting of V^m ∧ Vⁿ for a prime p ≥ 5. The proof is based on explicit calculations of [V^n+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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