Laura P. Schaposnik

Real structures on moduli spaces of Higgs bundles

We construct triples of commuting real structures on the moduli space of Higgs bundles, whose fixed loci are branes of type (B, A, A), (A, B, A) and (A, A, B). We study the real points through the associated spectral data and describe the topological invariants involved using KO, KR and equivariant K-theory.

Higgs Bundles and (A, B, A)-Branes

Through the action of anti-holomorphic involutions on a compact Riemann surface Σ we construct families of (A, B, A)-branes

Spectral Data for U(m,m)-Higgs Bundles

{\mathcal{L}_{G_{c}}}

Branes through finite group actions

LGc in the moduli spaces

A geometric approach to orthogonal Higgs bundles

{\mathcal{M}_{G_{c}}}

Automorphisms of C Moduli Spaces Associated to a Riemann Surface

MGc of Gc-Higgs bundles on Σ. We study the geometry of these (A, B, A)-branes in terms of spectral data and show they have the structure of real integrable systems.