Curvature and characteristic numbers of hyper-Kähler manifolds (Q1847807)

In the paper under review the characteristic numbers of compact hyper-Kähler manifolds are expressed in graph-theoretical form, considering them as a special case of the curvature invariants introduced by \textit{L. Rozansky} and \textit{E. Witten} [Sel. Math., New Ser. 3, 401-458 (1997; Zbl 0908.53027)]. The appropriate graphs are generated by ``wheels'', and the recently proved Wheeling theorem is used to give a formula for the \({\mathcal L}^2\)-norm of the curvature of an irreducible hyper-Kähler manifold in terms of the volume and Pontryagin numbers. The formula involves the multiplicative sequence that is the square root of the \(\widetilde A\)-polynomial.