Malcev completion conjecture for the kernel of the evaluation map

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Let R=Z[t]R={\mathbb Z}[t] or R=Z[t,t−1]R={\mathbb Z}[t,t^{-1}], let K(R)K(R) be the kernel of the evaluation map SL2(R)→SL2(Z)SL_2(R)\to SL_2({\mathbb Z}), and let W{\mathcal W} be the kernel of the induced map from the relative completion G(R){\mathcal G}(R) to G(Z){\mathcal G}({\mathbb Z}). Malcev completion conjecture. The map

K(R)⟶WK(R)\longrightarrow {\mathcal W}

is the Malcev completion. The group W{\mathcal W} is prounipotent, providing some evidence for the conjecture, but the claim is presented as conjectural in the case n=2n=2.

References

Primary source

Kevin P. Knudson, “Relative completions of linear groups over Z[t] and Z[t,t^-1]”, arXiv:math/9801100 (1998).

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