Multiplicative properties of the current transform regulator
Abstract
This paper utilizes the properties of transforms of currents under equidimensional cycles, as introduced in MR4498559, to establish the multiplicative nature of the resulting regulator map, in the derived category. The construction relies on a synthetic presentation of the fundamental triples of currents from MR4498559, which exhibits group-like behavior under an extended Eilenberg-Zilber morphism. A key component of the analysis is a character of the permutation Hopf algebra that takes values in the function field of an infinite-dimensional affine space.
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