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Rozansky-Witten Wilson loop of unknot is A-hat genus

Contents

Contents

Statement

Proposition

(Rozansky-Witten Wilson loop observable of unknot is square root of A-hat genus)

For 4n\mathcal{M}^{4n} 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 A^( 4n)\sqrt{{\widehat A}(\mathcal{M}^{4n})} of the A-hat genus of 4n\mathcal{M}^{4n}.

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).

References

Review in

Created on January 1, 2020 at 12:40:09. See the history of this page for a list of all contributions to it.