The Kernel of the Equivariant Kirwan Map and the Residue Formula

2002/11/06 by Lisa C. Jeffrey, Jeffrey, Lisa C., Augustin-Liviu Mare +1
Mathematics · #58F05 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #math.DG #math.SG #msc:58F05

paper · pdf · doi:10.48550/arxiv.math/0211119

11 pages

arxiv created 2002/11/06 · openalex publication_date 2002/11/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using the notion of equivariant Kirwan map, as defined by Goldin, we prove that -- in the case of Hamiltonian torus actions with isolated fixed points -- Tolman and Weitsman's description of the kernel of the Kirwan map can be deduced directly from the residue theorem of Jeffrey and Kirwan. A characterization of the kernel of the Kirwan map in terms of residues of one variable (i.e. associated to Hamiltonian circle actions) is obtained.

Related

• The residue formula and the Tolman-Weitsman theorem
• The Kirwan map, equivariant Kirwan maps, and their kernels
• Integral Kirwan Surjectivity
• The biinvariant diagonal class for Hamiltonian torus actions
• An effective algorithm for the cohomology ring of symplectic reductions