turkmath.org

We will describe a construction of infinitesimal invariants of thickened   one dimensional cycles in three dimensional space, which are the simplest cycles that are not in the  Milnor range. 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.