Unstable Homotopy Invariance and the Homology of Sl 2 (zt])

We prove that if R is a domain with many units, then the natural inclusion E 2 (R) ! E 2 (Rt]) induces an isomorphism in integral homology. This is a consequence of the existence of an amalgamated free product decomposition of E 2 (Rt]). We also use this decomposition to study the homology of E 2 (Zt]) and show that a great deal of the homology of E 2 (Zt]) maps nontrivially into the homology of SL 2 (Zt]). As a consequence, we show that the latter is not nitely generated in all positive degrees.