Rozansky-Witten invariants of hyperkähler manifolds

Details Rozansky-Witten invariants of hyperkähler manifolds Rozansky-Witten invariants of hyperkähler manifolds

2004-04-20

arxiv.org/abs/math/0404360v1

Mathematics

Differential Geometry

Cambridge PhD thesis (2000), 130 pages, 5 figures

Scientific paper

We investigate invariants of compact hyperk{\"a}hler 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 hyperk{\"a}hler 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 hyperk{\"a}hler 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.

Affiliated with

Also associated with

No associations

Rating

Rozansky-Witten invariants of hyperkähler manifolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Rozansky-Witten invariants of hyperkähler manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Rozansky-Witten invariants of hyperkähler manifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-55778