Quantitative conditions for right-handedness

We give a numerical condition for right-handedness of a dynamically convex Reeb flow on S3. Our condition is stated in terms of an asymptotic ratio between the amount of rotation of the linearised flow and the linking number of trajectories with a periodic orbit that spans a disk-like global surface of section. As an application, we find an explicit constant δ∗ < 0.7225 such that if a Riemannian metric on the 2-sphere is δ-pinched with δ > δ∗, then its geodesic flow lifts to a right-handed flow on S3. In particular, all finite collections of periodic orbits of such a geodesic flow bind open books whose pages are global surfaces of section.

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