Holomorphic vector bundles, knots and the Rozansky-Witten invariants

Link invariants, for 3-manifolds, are defined in the context of the Rozansky-Witten theory. To each knot in the link one associates a holomorphic bundle over a holomorphic symplectic manifold X. The invariants are evaluated for b1 (M) ≥ 1 and X Hyper-Kaehler. To obtain invariants of Hyper-Kaehler X one finds that the holomorphic vector bundles must be hyper-holomorphic. This condition is derived and explained. Some results for X not Hyper-Kaehler are presented. (author)