Rationality theorems for curvature invariants of 2-complexes
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| Názov: | Rationality theorems for curvature invariants of 2-complexes |
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| Autori: | Wilton, H |
| Prispievatelia: | DSpace at Cambridge pro (8.1) |
| Zdroj: | Mathematische Annalen. 392:3765-3796 |
| Publication Status: | Preprint |
| Informácie o vydavateľovi: | Springer Science and Business Media LLC, 2025. |
| Rok vydania: | 2025 |
| Predmety: | Mathematics - Geometric Topology, 4901 Applied Mathematics, 4903 Numerical and Computational Mathematics, FOS: Mathematics, 49 Mathematical Sciences, 4904 Pure Mathematics, Geometric Topology (math.GT), Group Theory (math.GR), 0101 mathematics, Mathematics - Group Theory, 01 natural sciences |
| Popis: | Let X be a finite, 2-dimensional cell complex. The curvature invariants $$\rho _\pm (X)$$ ρ ± ( X ) and $$\sigma _\pm (X)$$ σ ± ( X ) were defined in [13], and a programme of conjectures was outlined. Here, we prove the foundational result that the quantities $$\rho _\pm (X)$$ ρ ± ( X ) and $$\sigma _\pm (X)$$ σ ± ( X ) are the extrema of explicit rational linear-programming problems. As a result they are rational, realised, and can be computed algorithmically. |
| Druh dokumentu: | Article |
| Popis súboru: | application/pdf; text/xml |
| Jazyk: | English |
| ISSN: | 1432-1807 0025-5831 |
| DOI: | 10.1007/s00208-025-03177-8 |
| DOI: | 10.17863/cam.117937 |
| DOI: | 10.48550/arxiv.2210.09841 |
| Prístupová URL adresa: | http://arxiv.org/abs/2210.09841 |
| Rights: | CC BY |
| Prístupové číslo: | edsair.doi.dedup.....d990474ea9b3da1c9462ffce3b8c9a24 |
| Databáza: | OpenAIRE |
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Nájsť tento článok vo Web of Science | Abstrakt: | Let X be a finite, 2-dimensional cell complex. The curvature invariants $$\rho _\pm (X)$$ ρ ± ( X ) and $$\sigma _\pm (X)$$ σ ± ( X ) were defined in [13], and a programme of conjectures was outlined. Here, we prove the foundational result that the quantities $$\rho _\pm (X)$$ ρ ± ( X ) and $$\sigma _\pm (X)$$ σ ± ( X ) are the extrema of explicit rational linear-programming problems. As a result they are rational, realised, and can be computed algorithmically. |
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| ISSN: | 14321807 00255831 |
| DOI: | 10.1007/s00208-025-03177-8 |