TY - JOUR
T1 - DkGravitational Instantons as Superpositions of Atiyah-Hitchin and Taub-NUT Geometries
AU - Schroers, B. J.
AU - Singer, M. A.
N1 - Publisher Copyright:
© 2021 The Author(s) 2021. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: [email protected].
PY - 2021/6
Y1 - 2021/6
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85108953014&partnerID=8YFLogxK
U2 - 10.1093/qmath/haab002
DO - 10.1093/qmath/haab002
M3 - Article
AN - SCOPUS:85108953014
SN - 0033-5606
VL - 72
SP - 277
EP - 337
JO - Quarterly Journal of Mathematics
JF - Quarterly Journal of Mathematics
IS - 1-2
ER -