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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 ...

What is the current state of knowledge of the group homology of $SL_2(k[t,t^{-1}])$? I am mostly interested in the case $k$ is algebraically closed of characteristic zero. The most recent work I am ...

I am trying to compute the group $H_1(\mathrm{SL}_2(\mathbb{Z}_2),M)$, where $\mathbb{Z}_2$ are $2$-adic integers and M is a module $\mathbb{Z}_2 \oplus \mathbb{Z}_2$. I suppose that the group acts ...