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(Rozansky-Witten Wilson loop observable of unknot is square root of A-hat genus)
For a hyperkähler manifold (or just a holomorphic symplectic manifold) the Rozansky-Witten invariant Wilson loop observable associated with the unknot in the 3-sphere is the square root of the A-hat genus of .
This is Roberts-Willerton 10, Lemma 8.6, using the Wheels theorem (Bar-Natan, Thang, Thurston 03) and the Hitchin-Sawon theorem (Hitchin-Sawon 99).
Dror Bar-Natan, Le Tu Quoc Thang, Dylan Thurston, Two applications of elementary knot theory to Lie algebras and Vassiliev invariants, Geom. Topol. Volume 7, Number 1 (2003), 1-31 (euclid.gt/1513883092)
Nigel Hitchin, Justin Sawon, Curvature and characteristic numbers of hyperkähler manifolds, Duke Math.J. 106 (2001) 599-615 (arXiv:math/9908114)
Justin Roberts, Simon Willerton, On the Rozansky-Witten weight systems, Algebr. Geom. Topol. 10 (2010) 1455-1519 (arXiv:math/0602653)
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