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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2301.10212 |
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| _version_ | 1866916341926068224 |
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| author | Nilsson, Gustav |
| author_facet | Nilsson, Gustav |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_10212 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Topology of Toric Gravitational Instantons Nilsson, Gustav Differential Geometry 53C25 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. |
| title | Topology of Toric Gravitational Instantons |
| topic | Differential Geometry 53C25 |
| url | https://arxiv.org/abs/2301.10212 |