Universal KZB Equations: The Elliptic Case

  title={Universal KZB Equations: The Elliptic Case},
  author={Damien Calaque and Benjamin Enriquez and Pavel Etingof},
  journal={arXiv: Quantum Algebra},
We define a universal version of the Knizhnik–Zamolodchikov–Bernard (KZB) connection in genus 1. This is a flat connection over a principal bundle on the moduli space of elliptic curves with marked points. It restricts to a flat connection on configuration spaces of points on elliptic curves, which can be used for proving the formality of the pure braid groups on genus 1 surfaces. We study the monodromy of this connection and show that it gives rise to a relation between the KZ associator and a… Expand
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