# General convergence criterion for a spectral sequence associated to a filtration of simplicial groups

Let $\cdots\subset F_r \subset \cdots \subset F_1 \subset F_0=G$ be a filtration of simplicial groups. If $\bigcap F_r$ is trivial, does the associated spectral sequence converge? If so, what does the associated spectral sequence converge to?

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Which associated spectral sequence? On homotopy groups? – Tyler Lawson Oct 24 '11 at 2:15