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

Contents

### Context

#### Knot theory

knot theory

Examples/classes:

Types

knot invariants

Related concepts:

category: knot theory

# Contents

## Statement

###### Proposition

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

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

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.