Eigenvalues of Products of Unitary Matrices and Lagrangian Involutions

2005/06/06 by Elisha Falbel, Falbel, Elisha, Richard A. Wentworth +1 · 1 citation
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #math.GT

paper · pdf · doi:10.48550/arxiv.math/0506100

35 pages, 2 figures, to appear in Topology

arxiv created 2005/06/06 · arxiv updated 2009/12/01

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.

Cited by

• Horn's problem in PU(n,1)

Related

• Complex Lagrangian embeddings of moduli spaces of vector bundles
• Eigenvalues of matrix products
• A moduli space of minimal affine Lagrangian submanifolds
• Lagrangian configurations and Hamiltonian maps
• Minimal submanifolds in spheres and complex-valued eigenfunctions