Higgs bundles on Sasakian manifolds

TL;DR

This paper extends a fundamental correspondence between Higgs bundles and flat connections from Kähler to Sasakian manifolds, enabling new insights into the fundamental groups of these manifolds.

Contribution

It generalizes the Donaldson-Corlette-Hitchin-Simpson correspondence to compact quasi-regular Sasakian manifolds, linking Higgs bundles and flat connections in this setting.

Findings

Establishes a correspondence on Sasakian manifolds

Translates Kähler group restrictions to Sasakian groups

Provides tools for studying fundamental groups of Sasakian manifolds

Abstract

We extend the Donaldson-Corlette-Hitchin-Simpson correspondence between Higgs bundles and flat connections on compact K\"ahler manifolds to compact quasi-regular Sasakian manifolds. A particular consequence is the translation of restrictions on K\"ahler groups proved using the Donaldson-Corlette-Hitchin-Simpson correspondence to fundamental groups of compact Sasakian manifolds.