All Questions

$\DeclareMathOperator\SL{SL}$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 ...

Update: As mentioned below, the answer to the original question is a strong No. However, the case of $\pi_4$ remains, and actually I think that this one would follow from Suslin's conjecture on ...

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) ...

Is it true that the universal cover of $\mathrm{SL}_2(\mathbb{R})$ has no non-trivial central extensions... as an abstract group? (that's certainly true as a Lie group) Motivation: I have a projective ...