Etesi, Gábor; Hausel, Tamás On Yang-Mills instantons over multi-centered gravitational instantons. (English) Zbl 1028.81039 Commun. Math. Phys. 235, No. 2, 275-288 (2003). Summary: In this paper we explicitly calculate the analogue of the ’t Hooft \(SU(2)\) Yang-Mills instantons on Gibbons-Hawking multi-centered gravitational instantons, which come in two parallel families: the multi-Eguchi-Hanson, or \(A_k\) ALE gravitational instantons and the multi-Taub-NUT spaces, or \(A_k\) ALF gravitational instantons. We calculate their energy and find the reducible ones. Following Kronheimer we also exploit the \(U(1)\) invariance of our solutions and study the corresponding explicit singular \(SU(2)\) magnetic monopole solutions of the Bogomolny equations on flat \(\mathbb R^3\). Cited in 1 ReviewCited in 19 Documents MSC: 81T13 Yang-Mills and other gauge theories in quantum field theory 83C57 Black holes 81V17 Gravitational interaction in quantum theory Keywords:’t Hooft SU(2) Yang-Mills instantons; Gibbons-Hawking multi-centered gravitational instantons; multi-Eguchi-Hanson or \(A_k\) ALE gravity instantons; multi-taub-NUT spaces PDFBibTeX XMLCite \textit{G. Etesi} and \textit{T. Hausel}, Commun. Math. Phys. 235, No. 2, 275--288 (2003; Zbl 1028.81039) Full Text: DOI arXiv