We prove a version of Sandon’s conjecture on the number of translated points of contactomorphisms for the case of prequantization bundles over certain closed monotone symplectic toric manifolds. Namely we show that any contactomorphism of such a 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 symplectic 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 integral symplectic toric manifolds to the context of prequantization bundles.

中文翻译：

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单调辛复曲面流形上预量化空间接触同构的平移点

对于某些闭合单调辛复曲面流形上的预量化束，我们证明了 Sandon 关于接触同胚平移点数的猜想的一个版本。也就是说，我们证明了位于接触同胚群的恒等分量中的这种预量化束的任何接触同胚至少具有 $N$ 个平移点，其中 $N$ 是辛复曲面流形的最小陈数。证明依赖于与等变上同调相结合的生成函数理论，据此我们将 Givental 的方法应用于积分辛复曲面流形的 Arnold 猜想，以适应预量化束的上下文。