Generalizations of Rozansky-Witten invariants

(with Justin Roberts)

Abstract

We survey briefly the definition of the Rozansky-Witten invariants, and review their relevance to the study of compact hyperkähler manifolds. We consider how various generalisations of the invariants might prove useful for the study of non-compact hyperkähler manifolds, of quaternionic-Kähler manifolds, and of relations between hyperkähler manifolds and Lie algebras. The paper concludes with a list of additional problems.

Appears in Vol. 4 (2002) of Geometry and Topology Monographs, Invariants of knots and 3-manifolds (Kyoto 2001), Paper no. 17 (available electronically). Also available as math.DG/0112210 from the e-Print archive.

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