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

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.

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Cited by in corpus (2)

• A real convexity theorem for quasi-hamiltonian actions
• Representations of the fundamental group of an L-punctured sphere generated by products of Lagrangian involutions