2004/12/10 by Ignasi Mundet-i-Riera, Mundet-i-Riera, Ignasi
Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.math/0412218
openalex publication_date 2004/12/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Suppose that an algebraic torus G acts algebraically on a projective manifold X with generically trivial stabilizers. Then the Zariski closure of the set of pairs \(x,y)∈ X× X| y=gx for someg∈ G\ defines a nonzero equivariant cohomology class [ΔG]∈ H^*G× G(X× X). We give an analogue of this construction in the case where X is a compact symplectic manifold endowed with a hamiltonian action of a torus, whose complexification plays the role of G. We also prove that the Kirwan map sends the class [ΔG] to the class of the diagonal in each symplectic quotient. This allows to define a canonical right inverse of the Kirwan map.