Reconstruction of Anosov flows from infinity

Every pseudo-Anosov flow in a closed 3-manifold M gives rise to an action of ₁ (M) on a circle S^1_ () from infinity Fen12, with a pair of invariant almost laminations. From certain actions on S^1 with invariant almost laminations, we reconstruct flows and manifolds realizing these actions, including all orientable transitive pseudo-Anosov flows in closed 3-manifolds. Denoting the Poincar\'e disk by D, our construction provides a geometry model for such flows and manifolds M by identifying the universal coverings of M with certain spaces induced from D D and identifying the action of ₁ (M) on S^1_ () with an action on D.