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YCor
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Reference Request: Finite models for torsion-free lattices

Let $G$ be a real, connected, semisimple Lie group and $\Gamma < G$ a torsion-free lattice. Then does there exist a finite $CW$-model for $B\Gamma$?

I know this to be true in many instances (e.g. when $\Gamma$ is uniform, when $G=SO_0(n,1)$$G=\mathrm{SO}_0(n,1)$ or when $rank_{\mathbb R}(G) \geq 2$$\mathrm{rank}_{\mathbb R}(G) \geq 2$ and $\Gamma$ is irreducible). In these instances, there always exist certain "canonical" finite CW-models for $B\Gamma$.

However, I am unaware of the situation for general such lattices, hence the question.

Reference Request: Finite models for torsion-free lattices

Let $G$ be a real, connected, semisimple Lie group and $\Gamma < G$ a torsion-free lattice. Then does there exist a finite $CW$-model for $B\Gamma$?

I know this to be true in many instances (e.g. when $\Gamma$ is uniform, when $G=SO_0(n,1)$ or when $rank_{\mathbb R}(G) \geq 2$ and $\Gamma$ is irreducible). In these instances, there always exist certain "canonical" finite CW-models for $B\Gamma$.

However, I am unaware of the situation for general such lattices, hence the question.

Finite models for torsion-free lattices

Let $G$ be a real, connected, semisimple Lie group and $\Gamma < G$ a torsion-free lattice. Then does there exist a finite $CW$-model for $B\Gamma$?

I know this to be true in many instances (e.g. when $\Gamma$ is uniform, when $G=\mathrm{SO}_0(n,1)$ or when $\mathrm{rank}_{\mathbb R}(G) \geq 2$ and $\Gamma$ is irreducible). In these instances, there always exist certain "canonical" finite CW-models for $B\Gamma$.

However, I am unaware of the situation for general such lattices, hence the question.

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H1ghfiv3
H1ghfiv3
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Reference Request: Finite models for torsion-free lattices

Let $G$ be a real, connected, semisimple Lie group and $\Gamma < G$ a torsion-free lattice. Then does there exist a finite $CW$-model for $B\Gamma$?

I know this to be true in many instances (e.g. when $\Gamma$ is uniform, when $G=SO_0(n,1)$ or when $rank_{\mathbb R}(G) \geq 2$ and $\Gamma$ is irreducible). In these instances, there always exist certain "canonical" finite CW-models for $B\Gamma$.

However, I am unaware of the situation for general such lattices, hence the question.