Tom Baird, Memorial University of Newfoundland
“The moduli space of Higgs bundles over a real curve and the real Abel-Jacobi ”
The moduli space MC of Higgs bundles over a complex curve X admits a hyperkahler metric: a Riemannian metric which is Kahler with respect to three different complex structures I, J, K, satisfying the quaternionic relations. If X admits an anti-holomorphic involution, then there is an induced involution on MC which is anti-holomorphic with respect to I and J, and holomorphic with respect to K. The fixed point set of this involution, MR, is therefore a real Lagrangian submanifold with respect to I and J, and complex symplectic with respect to K, making it a so called (A,A,B)-brane. In this talk, I will explain how to compute the Z2 Betti numbers of MR using Morse theory. A key role in this calculation is played by the Abel-Jacobi map from symmetric products of X to the Jacobian of X.
MC 5413