Betti numbers of the moduli space of rank 3 parabolic Higgs bundles
  We compute the Betti numbers of the moduli space of rank 3 parabolic Higgs bundles, using Morse theory. A key point is that certain critical submanifolds of the Morse function can be identified with moduli spaces of parabolic triples. These moduli spaces come in families depending on a real parameter and we study their variation with this parameter. 
O. Garc\'ia-Prada, P.B. Gothen and V. Mu\~noz