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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-Kahler. To obtain invariants of Hyper-Kahler X one finds that the holomorphic vector bundles must be hyper-holomorphic. This condition is derived and explained. Some results for X not Hyper-Kahler are presented.

Holomorphic vector bundles, knots and the Rozansky–Witten invariants