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Generalisations of Rozansky–Witten invariants

Justin Roberts and Justin Sawon

Geometry & Topology Monographs 4 (2002) 263–279

DOI: 10.2140/gtm.2002.4.263

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.

Keywords

hyperkähler manifold, quaternion–Kähler manifold

Mathematical Subject Classification

Primary: 53C26, 57R20

Secondary: 57M27

References
Publication

Received: 3 December 2001
Revised: 1 April 2002
Accepted: 22 July 2002
Published: 13 October 2002

Authors
Justin Roberts
Department of Mathematics
UC San Diego
9500 Gilman Drive
La Jolla CA 92093
USA
http://www.math.ucsd.edu/~justin/
Justin Sawon
Mathematical Institute
24–29 St Giles' Oxford OX1 3BN
UK
http://www.maths.ox.ac.uk/~sawon/