Rozansky-Witten invariants via formal geometry

TL;DR

This paper connects Rozansky-Witten invariants to characteristic classes of foliations and Gelfand-Fuks cohomology, revealing new ways to derive invariants of 3-manifolds and hyperkähler manifolds.

Contribution

It demonstrates that Rozansky-Witten invariants originate from characteristic classes of foliations and Gelfand-Fuks cohomology, providing a new geometric perspective.

Findings

Invariants of 3-manifolds derived from symplectic foliations.

Connection established between Rozansky-Witten invariants and characteristic classes.

Intersections with existing work by Kapranov on related invariants.

Abstract

We show that recently constructed invariants of 3-dimensional manifolds and of hyperkaehler manifolds (L.Rozansky and E.Witten, hep-th/9612216) come from characteristic classes of foliations and from Gelfand-Fuks cohomology. In particular, any symplectic foliation gives invariants of 3-manifolds. Our preprint has many intersections with the preprint alg-geom/9704009 by M.Kapranov.