Jump formulas in Hamiltonian Geometry

2004/11/13 by Paul-Emile Paradan, Paradan, Paul-Emile
Mathematics · #FOS: Mathematics #Group Theory (math.GR) #Symplectic Geometry (math.SG) #math.GR #math.SG

paper · pdf · doi:10.48550/arxiv.math/0411306

Latex, 40 pages

arxiv created 2004/11/13 · arxiv updated 2009/12/01

Abstract

This paper is concerned with the Hamiltonian actions of a torus on a symplectic manifold. We are interested here in two global invariants: the Duistermaat-Heckman measure DH(M), and the Riemann-Roch chatacters RR(M,L^k),k>0, which are defined when the symplectic manifold is prequantized by a Kostant-Souriau line bundle L. We can associate to each connected component C of regular values of the moment map the following local invariants: the polynomial DH_c which coincides with DH(M) on C, and the periodic polynomial m_c which computes the multiplicity of RR(M,L^k), k>0, in the cone generated by C. The purpose of this paper is to compute the differences DH_c - DH_c' and m_c - m_c' when C and C' are two adjacent connected components of regular values of the moment map.

Related

• Restriction of the moment map to certain non-Lagrangian submanifolds
• Complete invariants for Hamiltonian torus actions with two dimensional quotients
• Duistermaat-Heckman measures for Hamiltonian groupoid actions
• Centered complexity one Hamiltonian torus actions
• Simple Hamiltonian manifolds