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Importance of third homology of $\operatorname{SL}_{2}$ over a field
$\DeclareMathOperator\SL{SL}$I am reading some papers about the third homology of linear groups. In particular for the $\SL_{2}$ over a field. Why is it important to study these homologies?
I have ...
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Non-existence of nontrivial finite group extension of any simply-connected Lie group
Let $Q$ be a simply-connected compact Lie group. Can one outline the proof (or provide the counter examples if my statement is false) that
there does not exist any group $G$ (with no topology) ...
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