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Displaying similar documents to “Hyperkähler manifolds”

Geometric quantization and no-go theorems

Viktor Ginzburg, Richard Montgomery (2000)

Banach Center Publications

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A geometric quantization of a Kähler manifold, viewed as a symplectic manifold, depends on the complex structure compatible with the symplectic form. The quantizations form a vector bundle over the space of such complex structures. Having a canonical quantization would amount to finding a natural (projectively) flat connection on this vector bundle. We prove that for a broad class of manifolds, including symplectic homogeneous spaces (e.g., the sphere), such connection does not exist....

On Seiberg-Witten equationsοn symplectic 4-manifolds

Klaus Mohnke (1997)

Banach Center Publications

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We discuss Taubes' idea to perturb the monopole equations on symplectic manifolds to compute the Seiberg-Witten invariants in the light of Witten's symmetry trick in the Kähler case.