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arXiv · 2107.13626

An Infinite Dimensional Virtual Cohomology Group of $\textbf{SL}_3(\mathbb{Z}[t])$

Matthew Goroff
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Abstract

We prove that $\textbf{SL}_3(\mathbb{Z}[t])$ has a finite index subgroup $\Gamma$ such that $H^2(\Gamma; \mathbb{Q})$ is infinite dimensional. The proof uses the geometry of the Euclidean building for $\textbf{SL}_3(\mathbb{Q}((t^{-1})))$.

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Matthew Goroff. 2021-07-28. An Infinite Dimensional Virtual Cohomology Group of $\textbf{SL}_3(\mathbb{Z}[t])$. https://arxiv.org/abs/2107.13626

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