论文标题
$ d_k $引力instantons作为atiyah-hitchin和taub-nut几何形状的叠加
$D_k$ Gravitational Instantons as Superpositions of Atiyah-Hitchin and Taub-NUT Geometries
论文作者
论文摘要
我们通过一种粘合结构获得了$ d_k $ alf重力激体孔，该结构以精确且明确的方式捕获，其解释为中心的$ su（2）$单孔的非线性叠加，配备了Atiyah-Hitchin Monopoles，并配备了Atiyah-Hitchin Metric，以及taub-nut-nutricold copies of atiyah-hitchin monopoles。构造从欧几里得空间中的一组有限点进行，对原点的反射对称，并取决于绝热参数，该参数被纳入几何形状，作为第五维。使用一个与边界的多种歧管上的甲状化三元组合的配方，我们表明成分的atiyah-hitchin和taub-nut几何形状是5维几何形状的边界成分，因为将绝热参数视为零。
We obtain $D_k$ ALF gravitational instantons by a gluing construction which captures, in a precise and explicit fashion, their interpretation as non-linear 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 5-dimensional geometry as the adiabatic parameter is taken to zero.
