Reconstruction of Anosov flows from infinity

2024/07/10 by Baik, Hyungryul, Wu, Chenxi, Zhao, Bojun · 2 citations
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2407.07634

Abstract

Every pseudo-Anosov flow ϕ in a closed 3-manifold M gives rise to an action of π₁(M) on a circle S¹_∞(ϕ) from infinity \citeFen12, with a pair of invariant almost laminations. From certain actions on S¹ with invariant almost laminations, we reconstruct flows and manifolds realizing these actions, including all orientable transitive pseudo-Anosov flows in closed 3-manifolds. Our construction provides a geometry model for such flows and manifolds induced from D × D, where D is the Poincaré disk with ∂ D identified with S¹_∞(ϕ). In addition, our result applies to Cannon conjecture under the assumption that certain group-equivariant sphere-filling Peano curve exists, which offers a description of orientable quasigeodesic pseudo-Anosov flows in hyperbolic 3-manifolds in terms of group actions on ∂ ℍ³ × ∂ ℍ³ × ∂ ℍ³.

Cited by

• Universal circles for Anosov foliations
• Reconstructing flows from the orbit space

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