2007/05/07 by Florent Schaffhauser, Schaffhauser, Florent
Mathematics · #53D20 #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #math.SG #msc:53D20
paper · pdf · doi:10.48550/arxiv.0705.0858
25 pages
arxiv created 2007/05/07 · openalex publication_date 2007/05/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The main result of this paper is a quasi-hamiltonian analogue of a special case of the O'Shea-Sjamaar convexity theorem for usual momentum maps. We denote by U a simply connected compact connected Lie group and we fix an involutive automorphism of maximal rank on this Lie group (such an automorphism always exists). We then denote by M a quasi-hamiltonian U-space and we prove that the image under the momentum map of the fixed-point set of a form-reversing compatible involution of M is a convex polytope, which is in fact equal to the full momentum polytope. This theorem was announced in arXiv:math/0609517v1. As an application, we obtain an example of lagrangian subspace in representation spaces of surface groups.