Rationality theorems for curvature invariants of 2-complexes
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866916707998629888 |
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| author | Wilton, Henry |
| author_facet | Wilton, Henry |
| contents | Let $X$ be a finite, 2-dimensional cell complex. The curvature invariants $ρ_\pm(X)$ and $σ_\pm(X)$ were defined in [13], and a programme of conjectures was outlined. Here, we prove the foundational result that the quantities $ρ_\pm(X)$ and $σ_\pm(X)$ are the extrema of explicit rational linear-programming problems. As a result they are rational, realised, and can be computed algorithmically. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_09841 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Rationality theorems for curvature invariants of 2-complexes Wilton, Henry Group Theory Geometric Topology Let $X$ be a finite, 2-dimensional cell complex. The curvature invariants $ρ_\pm(X)$ and $σ_\pm(X)$ were defined in [13], and a programme of conjectures was outlined. Here, we prove the foundational result that the quantities $ρ_\pm(X)$ and $σ_\pm(X)$ are the extrema of explicit rational linear-programming problems. As a result they are rational, realised, and can be computed algorithmically. |
| title | Rationality theorems for curvature invariants of 2-complexes |
| topic | Group Theory Geometric Topology |
| url | https://arxiv.org/abs/2210.09841 |