Construction of gravitational instantons with non-maximal volume growth via codimension-1 collapse

2024/06/24 by Salm, Willem Adriaan
#53C25 #53C26 #53C55 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2406.16318

Abstract

In this paper, we construct families of gravitational instantons of type ALG, ALG*, ALH and ALH* using a gluing construction. Away from a finite set of exceptional points, the metric collapses with bounded curvature to a quotient of ℝ³ by ℤ₂ and a lattice of rank one or two. Depending on whether the gravitational instantons are of type ALG/ALG* or ALH/ALH*, there are either two or four exceptional points respectively that are modelled on the Atiyah-Hitchin manifold. The other exceptional points are modelled on the Taub-NUT metric. There are at most four, respectively eight, of these points in each case.

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