On the geometry of rod packings in the 3-torus

Connie On Yu Hui; Jessica S. Purcell

doi:10.1112/blms.12993

On the geometry of rod packings in the 3-torus

Connie On Yu Hui, Jessica S. Purcell

School of Mathematics

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

2 Citations (Scopus)

Abstract

Rod packings in the 3-torus encode information of some crystal structures in crystallography. They can be viewed as links in the 3-torus, and tools from 3-manifold geometry and topology can be used to study their complements. In this paper, we initiate the use of geometrisation to study such packings. We analyse the geometric structures of the complements of simple rod packings, and find families that are hyperbolic and Seifert fibred.

Original language	English
Pages (from-to)	1291-1309
Number of pages	19
Journal	Bulletin of the London Mathematical Society
Volume	56
Issue number	4
DOIs	https://doi.org/10.1112/blms.12993
Publication status	Published - Apr 2024

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10.1112/blms.12993Licence: CC BY-NC

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title = "On the geometry of rod packings in the 3-torus",

abstract = "Rod packings in the 3-torus encode information of some crystal structures in crystallography. They can be viewed as links in the 3-torus, and tools from 3-manifold geometry and topology can be used to study their complements. In this paper, we initiate the use of geometrisation to study such packings. We analyse the geometric structures of the complements of simple rod packings, and find families that are hyperbolic and Seifert fibred.",

author = "Hui, {Connie On Yu} and Purcell, {Jessica S.}",

note = "Funding Information: We thank Norman Do for the helpful discussions. Parts of this work were inspired by the Monash Honours thesis of Sargon Al‐Jeloo [ 3 ]. The research was partially supported by the Australian Research Council, Grant Number: DP210103136. We also thank the anonymous referee for their helpful comments, particularly around crystallographic notions. Publisher Copyright: {\textcopyright} 2024 The Authors. Bulletin of the London Mathematical Society is copyright {\textcopyright} London Mathematical Society.",

year = "2024",

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doi = "10.1112/blms.12993",

language = "English",

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N1 - Funding Information: We thank Norman Do for the helpful discussions. Parts of this work were inspired by the Monash Honours thesis of Sargon Al‐Jeloo [ 3 ]. The research was partially supported by the Australian Research Council, Grant Number: DP210103136. We also thank the anonymous referee for their helpful comments, particularly around crystallographic notions. Publisher Copyright: © 2024 The Authors. Bulletin of the London Mathematical Society is copyright © London Mathematical Society.

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N2 - Rod packings in the 3-torus encode information of some crystal structures in crystallography. They can be viewed as links in the 3-torus, and tools from 3-manifold geometry and topology can be used to study their complements. In this paper, we initiate the use of geometrisation to study such packings. We analyse the geometric structures of the complements of simple rod packings, and find families that are hyperbolic and Seifert fibred.

AB - Rod packings in the 3-torus encode information of some crystal structures in crystallography. They can be viewed as links in the 3-torus, and tools from 3-manifold geometry and topology can be used to study their complements. In this paper, we initiate the use of geometrisation to study such packings. We analyse the geometric structures of the complements of simple rod packings, and find families that are hyperbolic and Seifert fibred.

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On the geometry of rod packings in the 3-torus

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On the geometry of rod packings in the 3-torus

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