Decomposable representations and Lagrangian submanifolds of moduli spaces associated to surface groups
arXiv:math/0703869 · doi:10.1007/s00208-008-0241-4
Abstract
In this paper, we construct a Lagrangian submanifold of the moduli space associated to the fundamental group of a punctured Riemann surface (the space of representations of this fundamental group into a compact connected Lie group). This Lagrangian submanifold is obtained as the fixed-point set of an anti-symplectic involution defined on the moduli space. The notion of decomposable representation provides a geometric interpretation of this Lagrangian submanifold.