$H^2(SL_3(\mathbb{Z}[t]); \mathbb{Q})$ is infinite dimensional

Abstract

We prove that H 2 (SL 3 (Z[t]); Q) is infinite dimensional. The proof follows an outline similar to recent results by Cobb, Kelly, and Wortman, using the Euclidean building for SL 3 (Q((t −1 ))) and a Morse function from Bux-Köhl-Witzel.