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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 ≥ 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
© 2023 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY).

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