DkGravitational Instantons as Superpositions of Atiyah-Hitchin and Taub-NUT Geometries

B. J. Schroers*, M. A. Singer

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


We obtain Dk ALF gravitational instantons by a gluing construction which captures, in a precise and explicit fashion, their interpretation as nonlinear superpositions of the moduli space of centred SU(2) monopoles, equipped with the Atiyah-Hitchin metric, and k copies of the Taub-NUT manifold. The construction proceeds from a finite set of points in euclidean space, reflection symmetric about the origin, and depends on an adiabatic parameter which is incorporated into the geometry as a fifth dimension. Using a formulation in terms of hyperKähler triples on manifolds with boundaries, we show that the constituent Atiyah-Hitchin and Taub-NUT geometries arise as boundary components of the five-dimensional geometry as the adiabatic parameter is taken to zero.

Original languageEnglish
Pages (from-to)277-337
Number of pages61
JournalQuarterly Journal of Mathematics
Issue number1-2
Early online date17 Feb 2021
Publication statusPublished - Jun 2021

ASJC Scopus subject areas

  • General Mathematics


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