Topology of Toric Gravitational Instantons

Nilsson, Gustav

doi:10.1016/j.difgeo.2024.102171

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Topology of Toric Gravitational Instantons

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Nilsson, Gustav
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Nilsson, G. (2024). Topology of Toric Gravitational Instantons. Differential Geometry and its Application, 96: 102171. doi:10.1016/j.difgeo.2024.102171.

Cite as: https://hdl.handle.net/21.11116/0000-000C-834E-9

Abstract

For an asymptotically locally Euclidean (ALE) or asymptotically locally flat
(ALF) gravitational instanton $(M,g)$ with toric symmetry, we express the
signature of $(M,g)$ directly in terms of its rod structure. Applying
Hitchin$\unicode{x2013}$Thorpe-type inequalities for Ricci-flat ALE/ALF
manifolds, we formulate necessary conditions that the rod structures of toric
ALE/ALF instantons must satisfy, as a step toward a classification of such
spaces. Finally, we apply these results to the study of rod structures with
three turning points.