Abstract
We survey briefly the definition of the Rozansky-Witten invariants, and review their relevance to the study of compact hyperkahler manifolds. We consider how various generalisations of the invariants might prove useful for the study of non-compact hyperkahler manifolds, of quaternionicKahler manifolds, and of relations between hyperkahler manifolds and Lie algebras. The paper concludes with a list of additional problems. AMS Classification 53C26, 57R20; 57M27
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