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Holomorphic Vector Bundles, Knots and the Rozansky-Witten Invariants

George Thompson
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Abstract

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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George Thompson. 2001-10-31. Holomorphic Vector Bundles, Knots and the Rozansky-Witten Invariants. https://arxiv.org/abs/hep-th/0002168

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