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

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.