Homology, Homotopy and Applications

Volume 8 (2006)

Number 1

Unstable splitting of $V(1) ^ V(1)$ and its applications

Pages: 169 – 186

DOI: http://dx.doi.org/10.4310/HHA.2006.v8.n1.a5

Author

Takahisa Shiina (Department of Mathematical Sciences, Shinshu University, Matsumoto, Japan)

Abstract

Let $P^n(p)$ be an $n$-dimensional mod $p$ Moore space and $V^n$ be the mapping cone of an Adams map $A:P^{n-1}(p) \rightarrow P^{n-2p+1}(p)$. This paper gives an unstable splitting of $V^m \wedge V^n$ for a prime $p \geq 5$. The proof is based on explicit calculations of $[V^{n+2p-1},V^n]$. As an application, we define a Samelson product on $[V^*,\Omega X]$ and prove that it satisfies anticommutativity and the Jacobi identity.

Keywords

$V(1)$, Samelson product

2010 Mathematics Subject Classification

55P15, 55Q15

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