Geometry & Topology Monographs, Vol. 4 (2002),
Invariants of knots and 3-manifolds (Kyoto 2001),
Paper no. 17, pages 263--279.

Generalisations of Rozansky-Witten invariants

Justin Roberts, Justin Sawon

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.

Keywords. Hyperkahler manifold, quaternion-Kahler manifold

AMS subject classification. Primary: 53C26, 57R20. Secondary: 57M27.

E-print: arXiv:math.DG/0112210

Submitted to GT on 3 December 2001. (Revised 1 April 2002.) Paper accepted 22 July 2002. Paper published 13 October 2002.

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Justin Roberts, Justin Sawon
Department of Mathematics, UC San Diego
9500 Gilman Drive,La Jolla, CA 92093, USA
Mathematical Institute, 24-29 St Giles'
Oxford OX1 3BN, UK
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