Given a family of Kaehler manifolds, by looking at the cohomology we can construct the period mapping. What should be the analogue of the period mapping in non-abelian Hodge theory (i.e. if we look at the fundamental groups, rather than cohomology)?
Given a family of Kaehler manifolds, by looking at the cohomology we can construct the period mapping. What should be the analogue of the period mapping in non-abelian Hodge theory (i.e. if we look at the fundamental groups, rather than cohomology)?