The naturality in Kirwan's decomposition

Abstract

Let X be a compact symplectic manifold, K a compact group acting symplectically on X, and assume there is a moment map. In [3]. Kirwan defined a stratification on X, and showed that the associated spectral sequence degenerates. In this note, we ask whether this degeneration comes from a stable splitting of X into Thom spaces on the strata. One can also ask a related arithmetic question. Is it true that the splitting Kirwan discovered respects the action of Galois groups? Show more