2000/02/29 by George Thompson
Physics and Astronomy · Mathematics · #hep-th #math.GT
published as Adv.Theor.Math.Phys. 5 (2002) 457-481 · LaTeX, 21 pages. Added a section on the construction of hyper-holomorphic vector bundles, a reference and acknowledgements. Version to be published in Adv. in Theor. Phys
arxiv created 2001/10/31 · arxiv updated 2009/11/30
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.