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Geometric and canonical triangulations of highly twisted knots

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posted on 2023-03-15, 02:52 authored by Sophie Louise Ham

It is conjectured that every cusped hyperbolic 3-manifold admits a geometric triangulation, that is, it can be decomposed into positive volume ideal hyperbolic tetrahedra. In this thesis, we show that sufficiently highly twisted knots admit a geometric triangulation. In addition, by extending work of Gueritaud and Schleimer, we give quantified versions of this result for several infinite families of examples. Further, we show that many of these triangulations are in fact canonical.

History

Campus location

Australia

Principal supervisor

Jessica Purcell

Additional supervisor 1

Norm Do

Year of Award

2022

Department, School or Centre

Mathematics

Course

Doctor of Philosophy

Degree Type

DOCTORATE

Faculty

Faculty of Science

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