The paper constructs a twisted (ellipsitomic) version of the universal elliptic KZB connection and derives filtered formality for subgroups of the torus pure braid group.
Ellipsitomic Associators
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abstract
We develop a notion of ellipsitomic associators by means of operad theory. We take this opportunity to review the operadic point-of-view on Drinfeld associators and to provide such an operadic approach for elliptic associators too. We then show that ellipsitomic associators do exist, using the monodromy of the universal ellipsitomic KZB connection, that we introduced in a previous work. We finally relate the KZB ellipsitomic associator to certain Eisenstein series associated with congruence subgroups of $SL_2(\mathbb{Z})$, and to twisted elliptic multiple zeta values.
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On the universal ellipsitomic KZB connection
The paper constructs a twisted (ellipsitomic) version of the universal elliptic KZB connection and derives filtered formality for subgroups of the torus pure braid group.