The Associated Map of the Nonabelian Gauss-Manin Connection

TL;DR

This paper explicitly describes the isomonodromy flow in nonabelian cohomology, linking it to the Hitchin map's quadratic part, advancing understanding of nonabelian Gauss-Manin connections.

Contribution

It provides explicit formulas for the isomonodromy flow vector fields and relates them to the Hitchin map's quadratic component, a novel connection in nonabelian cohomology.

Findings

Explicit vector fields for the nonabelian isomonodromy flow

Relation between the flow and the quadratic part of the Hitchin map

Insights into the structure of the nonabelian Gauss-Manin connection

Abstract

The Gauss-Manin connection for nonabelian cohomology spaces is the isomonodromy flow. We write down explicitly the vector fields of the isomonodromy flow and calculate its induced vector fields on the associated graded space of the nonabelian Hogde filtration. The result turns out to be intimately related to the quadratic part of the Hitchin map.