Conformal blocks and the cohomology of configuration spaces of curves

TL;DR

This paper connects conformal blocks associated with punctured curves to the cohomology of configuration spaces, and compares the WZW connection with the Gauss-Manin connection, revealing deep geometric relationships.

Contribution

It provides a realization of conformal blocks within the cohomology of configuration spaces and compares two important connections in this geometric context.

Findings

Conformal blocks can be embedded into the cohomology of configuration spaces.

The WZW connection is explicitly compared to the Gauss-Manin connection.

New insights into the geometric structure of conformal blocks and their associated connections.

Abstract

We realize any space of conformal blocks attached to a punctured curve inside the cohomology of a configuration space of that curve and compare the WZW connection with the Gauss-Manin connection.