We prove the strong Suslin reciprocity law conjectured by A. Goncharov. The Suslin reciprocity law is a generalization of the Weil reciprocity law to higher Milnor $K$-theory. The Milnor $K$-groups can be identified with the top cohomology groups of the polylogarithmic motivic complexes; Goncharov's conjecture predicts the existence of a contracting homotopy underlying Suslin reciprocity. The main ingredient of the proof is a homotopy invariance theorem for the cohomology of the polylogarithmic motivic complexes in the ‘next to Milnor’ degree. We apply these results to the theory of scissors congruences of hyperbolic polytopes. For every triple of rational functions on a compact projective curve over $\mathbb {C}$ we construct a hyperbolic polytope (defined up to scissors congruence). The hyperbolic volume and the Dehn invariant of this polytope can be computed directly from the triple of rational functions on the curve.

我们证明了冈萨洛夫（A. Goncharov）推测的强大的Suslin互惠律。Suslin互惠定律是Weil互惠定律的推广，适用于较高的Milnor $ K $理论。可以将Milnor $ K $ -群与多对数动机复合体的最高同调群识别；贡恰洛夫的猜想预言了苏斯林互惠性存在着一种同质性收缩现象。证明的主要成分是同位不变定理，用于多对数动机复合体的“同构”，即“弥尔诺”级。我们将这些结果应用于双曲线多面体的剪刀全等理论。对于$ \ mathbb {C} $上的紧致投影曲线上的每三个有理函数我们构建了一个双曲线多面体（定义为剪刀全等）。可以从曲线上的三重有理函数直接计算出该多态性的双曲体积和Dehn不变性。