Eigenvalues of Products of Unitary Matrices and Lagrangian Involutions

Abstract

This 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 Topology