The Kernel of the Equivariant Kirwan Map and the Residue Formula
نویسنده
چکیده
Using the notion of equivariant Kirwan map, as defined by Goldin [3], 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 [6] and [7]. 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.
منابع مشابه
The residue formula and the Tolman-Weitsman theorem
We give a simple direct proof (for the case of Hamiltonian circle actions with isolated fixed points) that Tolman and Weitsman’s description of the kernel of the Kirwan map in [9] (in other words the sum of those equivariant cohomology classes vanishing on one side of a collection of hyperplanes) is equivalent to the characterization of this kernel given by the residue theorem [6].
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