Oriented Birkhoff sections of Anosov flows

TL;DR

This paper proves that for Anosov flows on oriented 3-manifolds, the existence of a positive Birkhoff section is equivalent to the flow being -covered positively twisted, providing three independent proofs of this fact.

Contribution

It offers three independent proofs establishing the equivalence between positive Birkhoff sections and -covered positively twisted Anosov flows.

Findings

Positive Birkhoff sections exist if and only if the flow is -covered positively twisted

Three independent proofs confirm the equivalence

Characterizes a specific class of Anosov flows

Abstract

This paper gives 3 different proofs (independently obtained by the 3 authors) of the following fact: given an Anosov flow on an oriented 3 manifold, the existence of a positive Birkhoff section is equivalent to the fact that the flow is $\mathbb{R}$-covered positively twisted.