K. Morisugi
Hopf constructions, Samelson products and suspension maps

Abstract: Let $\alpha\in\pi_p(X)$ and $\beta\in\pi_q(X)$ for an H- space $(X, \mu)$. In this paper we will observe the relation between $\langle E\alpha, E\beta\rangle$ and $E\langle\alpha, \beta\rangle$, where $E: X \to \Omega\Sigma X$ is the suspension map and $\langle\quad, \quad\rangle$ is the Samelson product. Actually, the relation can be described by using the "generalized Hopf constructions". As an application, we determine the group $[\Sigma Sp(2), \Sigma Sp(2)]$.

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