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Torus knot groups are certainly linear. The universal cover of a torus knot complement is Euclidean space, and the action of the group on this cover factors through "translations on euclidean space" cross $PSL_2(\mathbb R)$. Both linear groups.

Generally it's conjectured that all 3-manifold groups are linear. For all I know, there might be a proof already. See What is known about a 3-manifold $M$ when its fundamental group is linear?What is known about a 3-manifold $M$ when its fundamental group is linear?

Torus knot groups are certainly linear. The universal cover of a torus knot complement is Euclidean space, and the action of the group on this cover factors through "translations on euclidean space" cross $PSL_2(\mathbb R)$. Both linear groups.

Generally it's conjectured that all 3-manifold groups are linear. For all I know, there might be a proof already. See What is known about a 3-manifold $M$ when its fundamental group is linear?

Torus knot groups are certainly linear. The universal cover of a torus knot complement is Euclidean space, and the action of the group on this cover factors through "translations on euclidean space" cross $PSL_2(\mathbb R)$. Both linear groups.

Generally it's conjectured that all 3-manifold groups are linear. For all I know, there might be a proof already. See What is known about a 3-manifold $M$ when its fundamental group is linear?

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Ryan Budney
Ryan Budney
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Torus knot groups are certainly linear. The universal cover of a torus knot complement is Euclidean space, and the action of the group on this cover factors through "translations on euclidean space" cross $PSL_2(\mathbb R)$. Both linear groups.

Generally it's conjectured that all 3-manifold groups are linear. For all I know, there might be a proof already. See What is known about a 3-manifold $M$ when its fundamental group is linear?