Holomorphic Vector Bundles, Knots and the Rozansky-Witten Invariants

Details Holomorphic Vector Bundles, Knots and the Rozansky-Witten Invariants Holomorphic Vector Bundles, Knots and the Rozansky-Witten Invariants

2000-02-21

arxiv.org/abs/hep-th/0002168v3

Adv.Theor.Math.Phys. 5 (2002) 457-481

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX, 21 pages. Added a section on the construction of hyper-holomorphic vector bundles, a reference and acknowledgements. Ve

Scientific paper

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 b_{1}(M) \geq 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.

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