PhD Thesis: Rozansky-Witten invariants of hyperkähler manifolds

Abstract

We investigate invariants of compact hyperkähler manifolds introduced by Rozansky and Witten: they associate an invariant to each graph homology class. It is obtained by using the graph to perform contractions on a power of the curvature tensor and then integrating the resulting scalar-valued function over the manifold, arriving at a number. For certain graph homology classes, the invariants we get are Chern numbers, and in fact all characteristic numbers arise in this way.

We use relations in graph homology to study and compare these hyperkähler manifold invariants. For example, we show that the norm of the Riemann curvature can be expressed in terms of the volume and characteristic numbers of the hyperkähler manifold. We also investigate the question of whether the Rozansky-Witten invariants give us something more general than characteristic numbers. Finally, we introduce a generalization of these invariants which incorporates holomorphic vector bundles into the construction.

Available as math.DG/0404360 from the e-Print archive.

Back to the main page.

This page last modified by Justin Sawon
Wednesday, 21-Apr-2004 19:25:59 EDT
Email corrections and comments to sawon@math.sunysb.edu