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arXiv · 2301.10212

Topology of Toric Gravitational Instantons

Gustav Nilsson
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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, as a step toward a classification of toric ALE/ALF instantons, necessary conditions that the rod structures of such spaces must satisfy. Finally, we apply these results to the study of rod structures with three turning points.

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Gustav Nilsson. 2023-01-24. Topology of Toric Gravitational Instantons. https://doi.org/10.1016/j.difgeo.2024.102171

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