A higher dimensional version of Fáry's theorem

Karim Adiprasito; Zuzana Patáková

doi:10.1112/blms.70036

A higher dimensional version of Fáry's theorem

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Abstract

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

Original language	English
Pages (from-to)	1409-1414
Number of pages	6
Journal	Bulletin of the London Mathematical Society
Volume	57
Issue number	5
DOIs	https://doi.org/10.1112/blms.70036
State	Published - May 2025
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics

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abstract = "We prove a generalization of Istv{\'a}n F{\'a}ry's celebrated theorem to higher dimensions. Namely, we show that if a finite simplicial complex (Formula presented.) can be piecewise linearly embedded into a (Formula presented.) -dimensional PL manifold (Formula presented.), then there is a triangulation of (Formula presented.) containing (Formula presented.) as a subcomplex.",

author = "Karim Adiprasito and Zuzana Pat{\'a}kov{\'a}",

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

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DO - 10.1112/blms.70036

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EP - 1414

JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

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A higher dimensional version of Fáry's theorem

Abstract

All Science Journal Classification (ASJC) codes

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