Dokument

Summary:
We develop a novel approach to the topology of singular symplectic quotients by extending Sjamaar’s complex of differential forms to the complex of resolution differential forms. The motivation for this is to extend Sjamaar’s complex in a way which makes the definition of a Kirwan map possible. In his theory this is not possible due to the singularities of any connection form at the fixed points of the action. Thus, the idea is to resolve the group action by blow-ups. Doing this using real blow-ups results in a locally free action on the whole manifold but also in difficult exceptional bundles. Carrying out the construction using symplectic blow-ups the exceptional bundles turn out to be more controllable. This approach then allows to define a Kirwan map, whose surjectivity we study in case that the fixed point set has vanishing cohomology in odd degrees. It turns out that this map is surjective in even degrees while it is not surjective in odd degrees.

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