Simplicial Abel-Jacobi maps and reciprocity laws

We describe an explicit morphism of complexes that induces the cycle-class maps from (simplicially described) higher Chow groups to rational Deligne cohomology. The reciprocity laws satisfied by the currents we introduce for this purpose are shown to provide a clarifying perspective on functional equations satisfied by complex-valued di- and trilogarithms.
Comment: 51 pages, 1 figure; appendix by Burgos Gil added