The biinvariant diagonal class for Hamiltonian torus actions

dc.creatorMundet-i-Riera, Ignasi
dc.date2004-12-10
dc.date2006-11-09
dc.date.accessioned2026-07-07T06:39:09Z
dc.date.available2026-07-07T06:39:09Z
dc.descriptionSuppose 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 $\{(x,y)\in X\times X\mid y=gx \text{for some}g\in G\}$ defines a nonzero equivariant cohomology class $[Δ_G]\in H^*_{G\times G}(X\times X)$. 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 $[Δ_G]$ to the class of the diagonal in each symplectic quotient. This allows to define a canonical right inverse of the Kirwan map.
dc.descriptionA substatially revised version of the paper "A right inverse to the Kirwan map". Improved exposition. Singular quotients are also considered in the new version. 23 pages. Accepted for publication in Adv. in Math
dc.identifierhttps://arxiv.org/abs/math/0412218
dc.identifierhttp://arxiv.org/abs/math/0412218
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/100977
dc.subjectSymplectic Geometry
dc.titleThe biinvariant diagonal class for Hamiltonian torus actions
dc.typetext

Files

Collections