Relying on the theory of agrarian invariants introduced in previous work, we solve a conjecture of Friedl–Tillmann: we show that the marked polytopes they constructed for two‐generator one‐relator groups with nice presentations are independent of the presentations used. We also show that, when the groups are additionally torsion‐free, the agrarian polytope encodes the splitting complexity of the group. This generalises theorems of Friedl–Tillmann and Friedl–Lück–Tillmann.

中文翻译：

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两发电机单人组的农业多面体

依靠先前工作中介绍的耕地不变量理论，我们解决了弗里德尔-蒂尔曼的一个猜想：我们表明，他们为两发电机单人组构建的标记多面体表现出色，与所使用的表现形式无关。我们还表明，当这些组另外没有扭转时，耕地多角体编码了该组的分裂复杂性。这概括了Friedl–Tillmann和Friedl–Lück–Tillmann的定理。