We construct infinitesimal invariants of thickened one dimensional cycles in three dimensional space, which are the simplest cycles that are not in the Milnor range. This generalizes Park’s work on the regulators of additive cycles. The construction also allows us to prove the infinitesimal version of the strong reciprocity conjecture for thickenings of all orders. Classical analogs of our invariants are based on the dilogarithm function and our invariant could be seen as their infinitesimal version. Despite this analogy, the infinitesimal version cannot be obtained from their classical counterparts through a limiting process.

中文翻译：

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截断多项式环上曲线上的无穷小二对数

我们在三维空间中构造了加厚一维循环的无穷小不变量，这是不在 Milnor 范围内的最简单的循环。这概括了 Park 在添加剂循环调节器方面的工作。该构造还使我们能够证明所有阶增厚的强互易猜想的无穷小版本。我们的不变量的经典模拟是基于双对数函数，并且我们的不变量可以被视为它们的无穷小版本。尽管有这样的类比，无穷小版本无法通过限制过程从经典版本中获得。