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- W2238405649 abstract "A polynomial assignment for a continuous action of a compact torus $T$ on a topological space $X$ assigns to each $pin X$ a polynomial function on the Lie algebra of the isotropy group at $p$ in such a way that a certain compatibility condition is satisfied. The space ${mathcal{A}}_T(X)$ of all polynomial assignments has a natural structure of an algebra over the polynomial ring of ${rm Lie}(T)$. It is an equivariant homotopy invariant, canonically related to the equivariant cohomology algebra. In this paper we prove various properties of ${mathcal{A}}_T(X)$ such as Borel localization, a Chang-Skjelbred lemma, and a Goresky-Kottwitz-MacPherson presentation. In the special case of Hamiltonian torus actions on symplectic manifolds we prove a surjectivity criterion for the assignment equivariant Kirwan map corresponding to a circle in $T$. We then obtain a Tolman-Weitsman type presentation of the kernel of this map." @default.
- W2238405649 created "2016-06-24" @default.
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- W2238405649 date "2015-12-21" @default.
- W2238405649 modified "2023-09-27" @default.
- W2238405649 title "Assignments for topological group actions" @default.
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