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arXiv · 2210.09841

Rationality theorems for curvature invariants of 2-complexes

Henry Wilton
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Abstract

Let $X$ be a finite, 2-dimensional cell complex. The curvature invariants $\rho_\pm(X)$ and $\sigma_\pm(X)$ were defined in [13], and a programme of conjectures was outlined. Here, we prove the foundational result that the quantities $\rho_\pm(X)$ and $\sigma_\pm(X)$ 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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Henry Wilton. 2022-10-18. Rationality theorems for curvature invariants of 2-complexes. https://arxiv.org/abs/2210.09841

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