Higgs bundles for the Lorentz group

TL;DR

This paper proves that the moduli space of SO_0(1,n)-Higgs bundles with odd n has exactly two connected components, using Morse-theoretic methods introduced by Hitchin.

Contribution

It establishes the topological structure of the moduli space for SO_0(1,n)-Higgs bundles when n is odd, revealing its two connected components.

Findings

The moduli space of SO_0(1,n)-Higgs bundles has two connected components for odd n.

Morse-theoretic methods can be effectively applied to study Higgs bundle moduli spaces.

The result advances understanding of the topology of Higgs bundle moduli spaces for Lorentz groups.

Abstract

Using the Morse-theoretic methods introduced by Hitchin, we prove that the moduli space of $\SO_0(1,n)$-Higgs bundles when $n$ is odd has two connected components.