Generalisations of Rozansky-Witten invariants

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 quaternionic-Kahler manifolds, and of relations between hyperkahler manifolds and Lie algebras. The paper concludes with a list of additional problems.

Published by Geometry and Topology Monographs at http://www.maths.warwick.ac.uk/gt/GTMon4/paper17.abs.html