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Are there any interesting examples of relative CW complexes $ (X,A) $ where a map $ f \colon X_n \rightarrow Y $ into an abelian space has the property that the obstruction cocycle $ c_f $ is nonzero, but the class $ [c_f] $ is zero, so the restriction of the map $ f $ to the $ (n-1) $ skeleton can be extended to the $ (n+1) $ skeleton?

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