Hyperkahler manifolds and nonabelian Hodge theory of (irregular) curves

TL;DR

This paper provides a concise overview of hyperkahler manifolds and nonabelian Hodge theory for irregular curves, setting the stage for detailed future work on wild character varieties and irregular mapping class groups.

Contribution

It offers a survey of foundational results in hyperkahler geometry and nonabelian Hodge theory relevant to irregular curves and wild character varieties.

Findings

Background results on hyperkahler manifolds and nonabelian Hodge theory.

Context for wild character varieties and irregular mapping class groups.

Preparation for detailed future research on irregular curves.

Abstract

Short survey based on talk given at the Institut Henri Poincare January 17th 2012, during program on surface groups. The aim was to describe some background results before describing in detail (in subsequent talks) the results of [Boa11c] related to wild character varieties and irregular mapping class groups.