Fáry定理的高维版本

IF 0.8 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2025-02-27 DOI:10.1112/blms.70036

Karim Adiprasito, Zuzana Patáková

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引用次数: 0

摘要

我们证明了István Fáry著名定理在高维上的推广。也就是说，我们证明了如果一个有限简单复数X$ X$可以分段线性嵌入到d$ d$维PL流形M$ M$中，那么就有一个包含X$ X$作为子复数的M$ M$三角剖分。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

A higher dimensional version of Fáry's theorem

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A higher dimensional version of Fáry's theorem

We prove a generalization of István Fáry's celebrated theorem to higher dimensions. Namely, we show that if a finite simplicial complex $X$ can be piecewise linearly embedded into a $d$ -dimensional PL manifold $M$ , then there is a triangulation of $M$ containing $X$ as a subcomplex.