A geometric approach to orthogonal Higgs bundles
  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. 
Laura P. Schaposnik
math.AG math-ph math.DG math.MP