A geometric approach to orthogonal Higgs bundles

TL;DR

This paper introduces a geometric framework for understanding topological invariants of SO(m,m+1)-Higgs bundles using KO-theory and the Langlands correspondence, providing a new grading of their moduli space.

Contribution

It offers a novel geometric characterization of invariants and defines split orthogonal spectral data, advancing the understanding of Higgs bundle moduli spaces.

Findings

Topological invariants characterized via KO-theory

Natural grading of the moduli space established

Connection with Langlands correspondence demonstrated

Abstract

We give a geometric characterisation of the topological invariants associated to SO(m,m+1)-Higgs bundles through KO-theory and the Langlands correspondence between orthogonal and symplectic Hitchin systems. By defining the split orthogonal spectral data, we obtain a natural grading of the moduli space of SO(m,m+1)-Higgs bundles.