Each extended Cartan-Eilenberg system (H, ∂) gives rise to two exact couples and one spectral sequence. We show that the canonical colim-lim interchange morphism associated to H is a surjection, and that its kernel is isomorphic to Boardman's wholeplane obstruction group W , for each of the two exact couples.

We classify the singularities in the unframed Nakajima quiver varieties associated with extended Dynkin quivers and the corresponding minimal imaginary root with a small restriction on the parameters and use this to construct a number of hyper-Kähler cobordisms between binary polyhedral spaces.

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