## Homology, Homotopy and Applications

### Unstable splitting of V (1) \biwedge V and its applications

Takahisa. Shiina

#### 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 $V^m \bigwedge V ^n$ 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.

#### Article information

Source
Homology Homotopy Appl., Volume 8, Number 1 (2006), 169-186.

Dates
First available in Project Euclid: 15 February 2006

Permanent link to this document
https://projecteuclid.org/euclid.hha/1140012469

Mathematical Reviews number (MathSciNet)
MR2205217

Zentralblatt MATH identifier
1117.55003

#### Citation

Shiina, Takahisa. Unstable splitting of V (1) \biwedge V and its applications. Homology Homotopy Appl. 8 (2006), no. 1, 169--186. https://projecteuclid.org/euclid.hha/1140012469