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Can the fundamental group of a closed hyperbolic 3-manifold act freely on the plane by homeomorphisms? Freely and cocompactly? FreeFreely, cocompactcocompactly, and preserving orientation?

Can the fundamental group of a closed hyperbolic 3-manifold act freely on the plane? Freely and cocompactly? Free, cocompact, and preserving orientation?

Can the fundamental group of a closed hyperbolic 3-manifold act freely on the plane by homeomorphisms? Freely and cocompactly? Freely, cocompactly, and preserving orientation?

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Can the fundamental group of a closed hyperbolic 3-manifold act freely on the plane? Freely and cocompactly? Free, cocompact, and preserving orientation?

Can the fundamental group of a closed hyperbolic 3-manifold act freely on the plane? Freely and preserving orientation?

Can the fundamental group of a closed hyperbolic 3-manifold act freely on the plane? Freely and cocompactly? Free, cocompact, and preserving orientation?

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Can the fundamental group of a closed hyperbolic 3-manifold act freely on the plane? What about anFreely and preserving orientation-preserving action?

Can the fundamental group of a closed hyperbolic 3-manifold act freely on the plane? What about an orientation-preserving action?

Can the fundamental group of a closed hyperbolic 3-manifold act freely on the plane? Freely and preserving orientation?

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