对于每个非平面带状图，转子路由扭索和Bernardi扭索不一致
The rotor-routing torsor and the Bernardi torsor disagree for every non-planar ribbon graph
摘要：
设$G$为带状图。Matthew Baker和Yao Wang证明了当$G$为平面时，$G$的Rotor-Routing Torsor和Bernardi Torsor（它们是$G$的Picard群的生成树集合上的两个Torsor结构）重合.我们证明了他们提出的猜想，即当$G$是非平面的时候，两个Torsors不一致。
英文摘要：
Let $G$ be a ribbon graph. Matthew Baker and Yao Wang proved that the rotor-routing torsor and the Bernardi torsor for $G$, which are two torsor structures on the set of spanning trees for the Picard group of $G$, coincide when $G$ is planar. We prove the conjecture raised by them that the two torsors disagree when $G$ is non-planar.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
