A bstract We construct a topological Chern-Simons sigma model on a Riemannian threemanifold M with gauge group G whose hyperk?hler target space X is equipped with a G -action. Via a perturbative computation of its partition function, we obtain new topological invariants of M that define new weight systems which are characterized by both Lie algebra structure and hyperk?hler geometry. In canonically quantizing the sigma model, we find that the partition function on certain M can be expressed in terms of Chern-Simons knot invariants of M and the intersection number of certain G -equivariant cycles in the moduli space of G -covariant maps from M to X . We also construct supersymmetric Wilson loop operators, and via a perturbative computation of their expectation value, we obtain new knot invariants of M that define new knot weight systems which are also characterized by both Lie algebra structure and hyperk?hler geometry.
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