Holomorphic vector bundles, knots and the Rozansky-Witten invariants

Feb, 2000
21 pages
Published in:
  • Adv.Theor.Math.Phys. 5 (2002) 457-481
e-Print:
Report number:
  • IC-2000-9

Citations per year

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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.
  • gauge field theory: Yang-Mills
  • Chern-Simons term
  • fibre bundle
  • differential geometry: symplectic
  • knot theory
  • differential forms
  • analytic properties
  • charge: topological