Year: 2026
Type: preprint
Abstract: We study the cohomology of iterated Kummer extensions on the moduli space of five-pointed rational curves, continuing [arXiv:2609.19341, arXiv:2609.21356]. A two-dimensional shrinking construction compares the Betti presentations obtained from its five forgetful projections. The corresponding Hodge defects give pentagram relations, quadratic relations between coefficients of the Drinfeld associator, which are equivalent to the pentagon equation under group-likeness, normalization, and reversal. Under reversal and vanishing of pure-power coefficients, the relations imply shuffle and regularized double shuffle, whose Hodge realization is recovered by a convolution specialization.
Source: arXiv (Cornell University)
Author: Markarian, Nikita
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7216462158