Homotopy transfer theorem and KZB connections

TL;DR

This paper demonstrates how the homotopy transfer theorem can be used to construct the KZB connection on punctured tori and their configuration spaces, linking homotopy theory with complex geometric connections.

Contribution

It introduces a novel application of the homotopy transfer theorem to explicitly construct KZB connections on punctured tori.

Findings

KZB connection can be derived via homotopy transfer theorem

Provides a new perspective on the relationship between homotopy theory and geometric connections

Establishes a method for constructing connections on configuration spaces

Abstract

We show that the KZB connection on the punctured torus and on the configuration space of points of the punctured torus can be constructed via the homotopy transfer theorem.