Decomposable representations and Lagrangian submanifolds of moduli spaces associated to surface groups

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/169787In 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.Symplectic Geometry53D20, 53D30Decomposable representations and Lagrangian submanifolds of moduli spaces associated to surface groupstext