Translated points for prequantization spaces over monotone toric manifolds

Abstract

We prove a version of Sandon's conjecture on the number of translated points of contactomorphisms for the case of a prequantization bundle over a closed monotone toric manifold. Namely we show that any contactomorphism of this prequantization bundle lying in the identity component of the contactomorphism group possesses at least $N$ translated points, where $N$ is the minimal Chern number of the toric manifold. The proof relies on the theory of generating functions coupled with equivariant cohomology, whereby we adapt Givental's approach to the Arnold conjecture for rational symplectic toric manifolds to the context of prequantization bundles.Comment: Corrected typos; added discussion in the introduction, explanations, and reference