Amalgamated Free Products, Unstable Homotopy Invariance, and the Homology of SL2(Z[t])

We prove that if R is a domain with many units, then the natural inclusion E2(R) → E2(R[t]) induces an isomorphism in integral homology. This is a consequence of the existence of an amalgamated free product decomposition of E2(R[t]). We also use this decomposition to study the homology of E2(Z[t]) and show that a great deal of the homology of E2(Z[t]) maps nontrivially into the homology of SL2(Z[t]). As a consequence, we show that the latter is not finitely generated in all positive degrees.