Geometric triangulations of a family of hyperbolic 3–braids

Nimershiem, Barbara

doi:10.2140/agt.2023.23.4309

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Geometric triangulations of a family of hyperbolic $3$–braids

Barbara Nimershiem

Algebraic & Geometric Topology 23 (2023) 4309–4348

DOI: 10.2140/agt.2023.23.4309

Abstract

We construct topological triangulations for complements of $(- 2, 3, n)$ –pretzel knots and links with $n \geq 7$ . Following a procedure outlined by Futer and Guéritaud, we use a theorem of Casson and Rivin to prove the constructed triangulations are geometric. Futer, Kalfagianni and Purcell have shown (indirectly) that such braids are hyperbolic. The new result here is a direct proof.

Keywords

hyperbolic links, geometric triangulations

Mathematical Subject Classification

Primary: 57K32

References

Publication

Received: 1 September 2021

Revised: 28 May 2022

Accepted: 21 June 2022

Published: 23 November 2023

Authors

Barbara Nimershiem
Department of Mathematics Franklin & Marshall College Lancaster, PA United States
https://www.fandm.edu/directory/barbara-nimershiem.html

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Volume 23, issue 9 (2023)