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

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

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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Bibliographische Detailangaben
Veröffentlicht in:	arXiv.org 2021-07
1. Verfasser:	Goroff, Matthew
Format:	Artikel
Sprache:	eng
Schlagworte:	Euclidean geometry Homology Subgroups
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	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 $\textbf{SL}_3(\mathbb{Q}((t^{-1})))$.
ISSN:	2331-8422

Zusammenfassung:	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 \(\textbf{SL}_3(\mathbb{Q}((t^{-1})))\).
ISSN:	2331-8422

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