Characterization of contact manifolds admitting Reeb pseudo-rotations in higher dimensions

Formulate and prove a precise characterization of higher-dimensional contact manifolds that admit Reeb pseudo-rotations, addressing the current lack of a rigorous statement of such a conjecture and a description of manifolds that do admit them.

Background

In dimension three, the so-called 2-or-infinity conjecture is essentially resolved, and lens spaces are the only manifolds admitting Reeb pseudo-rotations. In higher dimensions, the authors speculate that most tight or fillable contact manifolds may not admit Reeb pseudo-rotations, but they explicitly note the absence of a rigorous formulation and characterization.

This open direction seeks structural criteria for the existence (or nonexistence) of Reeb pseudo-rotations across higher-dimensional contact manifolds.