The Rotor-Routing Torsor and the Bernardi Torsor Disagree for Every Non-Planar Ribbon Graph
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.
2007 ◽
Vol 1
(1)
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pp. 265-275
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1992 ◽
Vol 105
(1-3)
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pp. 41-47
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2019 ◽
Vol 2019
(753)
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pp. 23-56
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