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.
arXiv Mathematics e-prints
- Pub Date:
- December 2001
- Mathematics - Differential Geometry;
- Mathematics - Quantum Algebra;
- Published by Geometry and Topology Monographs at http://www.maths.warwick.ac.uk/gt/GTMon4/paper17.abs.html