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

Karim Adiprasito, Zuzana Patáková^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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
Journal	Bulletin of the London Mathematical Society
DOIs	https://doi.org/10.1112/blms.70036
State	Accepted/In press - 2025
Externally published	Yes

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© 2025 The Author(s). Bulletin of the London Mathematical Society is copyright © London Mathematical Society.

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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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A higher dimensional version of Fáry's theorem

Abstract

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