2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75417This paper introduces a submanifold of the moduli space of unitary representations of the fundamental group of a punctured sphere with fixed local monodromy. The submanifold is defined via products of involutions through Lagrangian subspaces. We show that the moduli space of Lagrangian representations is a Lagrangian submanifold of the moduli of unitary representations.35 pages, 2 figures, to appear in TopologyGeometric Topologytext