Goodman-Fried surgery, Birkhoff section, and R-covered Anosov flows

2021/08/18 by Masayuki Asaoka, Asaoka, Masayuki
Computer Science · Mathematics · #37D20 (Primary) 37C86(Secondary) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2108.08215

openalex publication_date 2021/08/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we show that any topologically transitive Anosov flow on a closed three-dimensional manifold with the orientable weak stable and unstable foliations turns into an R-covered one by a Goodman-Fried surgery along periodic points. When a Birkhoff section of the Anosov flow is given, we can choose the periodic points from the boundary of the Birkhoff section.

Related

• Examples of Anosov flows with genus one Birkhoff sections
• Anosov flows on 3-manifolds: the surgeries and the foliations
• Oriented Birkhoff sections of Anosov flows
• Anosov flows on Dehn surgeries on the figure-eight knot
• R-covered foliations and transverse pseudo-Anosov flows in atoroidal pieces