Relative completions of linear groups over Z[t] and Z[t,t-1], by Kevin P. Knudson

In this paper we compute the completion of the groups SLn(Z[t]) and SLn(Z[t,t-1]) with respect to the obvious homomorphisms to SLn(Q); this is a generalization of the classical Malcev completion (which is trivial for these groups). It turns out that the obvious guess is the correct one, namely the proalgebraic group SLn(Q[[T]]). We use this result to study the rational second cohomology of the groups SLn(R) for R=Z[t], Z[t,t-1].

Kevin P. Knudson <>