Geometric triangulations of a family of hyperbolic 3-braids

Abstract

We construct topological triangulations for complements of $(-2,3,n)$-pretzel knots and links with $n\ge 7$. 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.

27 pages, 14 figures. V2: Improved exposition; additional figure; addresses referee comments. To appear in Algebraic & Geometric Topology

References in corpus (1)

• Geometric triangulations and highly twisted links