A construction of single-valued elliptic polylogarithms on the punctured elliptic curve is given that reduces to Brown's genus-zero condition upon torus degeneration.
Flat connections on configuration spaces and formality of braid groups of surfaces
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abstract
We construct an explicit bundle with flat connection on the configuration space of n points of a complex curve. This enables one to recover the `formality' isomorphism between the Lie algebra of the prounipotent completion of the pure braid group of n points on a surface and an explicitly presented Lie algebra t_{g,n} (Bezrukavnikov), and to extend it to a morphism from the full braid group of the surface to the semidirect product exp(hat t_{g,n}) rtimes S_n.
fields
hep-th 2years
2025 2verdicts
UNVERDICTED 2representative citing papers
Proves conjectural reformulation of motivic coaction and single-valued maps via zeta generators for multiple polylogarithms at genus zero on the Riemann sphere.
citing papers explorer
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A construction of single-valued elliptic polylogarithms
A construction of single-valued elliptic polylogarithms on the punctured elliptic curve is given that reduces to Brown's genus-zero condition upon torus degeneration.
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Deriving motivic coactions and single-valued maps at genus zero from zeta generators
Proves conjectural reformulation of motivic coaction and single-valued maps via zeta generators for multiple polylogarithms at genus zero on the Riemann sphere.