Oriented Birkhoff sections 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.

50 pages, 10 figures. New version: minor corrections and modifications, 4 new figures