5 papers · 1 filter
The framed version of the universal KZB connection in higher genera
Toyo Taniguchi
In this paper, the universal KZB connection on the configuration space of points on a closed Riemann surface of an arbitrary genus, introduced by Enriquez, is lifted to the configu…
Drinfeld associators and Kashiwara-Vergne associators in higher genera
Toyo Taniguchi
For , a genus Kashiwara-Vergne associator, introduced by Alekseev-Kawazumi-Kuno-Naef as a solution to the generalised KV equations in relation to the formality problem…
The formality of the Goldman-Turaev Lie bialgebra on a closed surface
Toyo Taniguchi
We reformulate the Kashiwara-Vergne groups and associators in higher genera, introduced in Alekseev-Kawazumi-Kuno-Naef, in terms of non-commutative connections using the tools deve…
A family of algebraic operations extending the Turaev cobracket
Toyo Taniguchi
We introduce a family of maps parametrised by certain ribbon graphs. It is based on a connection in non-commutative geometry and contains the double divergence as a special case. A…
Modular vector fields in non-commutative geometry
Toyo Taniguchi
We construct a non-commutative analogue of the modular vector field on a Poisson manifold for a given pair of a double bracket and a connection on a space of 1-forms. The key ingre…