Abstract
In this paper, we develop the new method to compute the homotopy groups of the mapping cone Cf=Y∪fCX beyond the metastable range by analysing the homotopy of the n-th filtration of the relative James construction J(X,A) for CW-pair A↪iX, defined by B. Gray, which is homotopy equivalent to the homotopy fiber of the pinch map X∪iCA→ΣA. As an application, we compute the 5 and 6-dim unstable homotopy groups of 3-dimensional mod 2r Moore spaces for all positive integers r.
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