Abstract

In this paper, we give an unstable approach of the May-Lawrence matrix Toda bracket, which becomes a useful tool to detect the unstable phenomena. Then, we give a generalization of the classical isomorphisms between homotopy groups of (JSm,Sm) and (JS2m,⁎) localized at 2. After that we provide a generalized H-formula for matrix Toda brackets. As an application, we show a new construction of κ¯′∈π26(S6) localized at 2 which improves the construction of κ¯′ given by [4].

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