Morse estimates for translated points on unit tangent bundles

Simon Allais

paper

Morse estimates for translated points on unit tangent bundles

arXiv:2205.13946

Abstract

In this article, we study conjectures of Sandon on the minimal number of translated points in the special case of the unit tangent bundle of a Riemannian manifold. We restrict ourselves to contactomorphisms of $S M$ that lift diffeomorphisms of $M$ homotopic to identity. We prove that there exist sequences $(p_{n}, t_{n})$ where $p_{n}$ is a translated point of time-shift $t_{n}$ with $t_{n} \to + \infty$ for a large class of manifolds. We also prove Morse estimates on the number of translated points in the case of Zoll Riemannian manifolds.

14 pages