Volume and geometry of homogeneously adequate knots

TL;DR

This paper establishes bounds on the hyperbolic volumes of homogeneously adequate knots and links using diagrammatic decomposition into ideal polyhedra and identifying essential product disks.

Contribution

It introduces volume bounds for a broad class of knots based on their diagrams and utilizes polyhedral decomposition and essential product disks.

Findings

Bounded hyperbolic volumes in terms of diagrams

Decomposed links into ideal polyhedra

Identified essential product disks in polyhedra

Abstract

We bound the hyperbolic volumes of a large class of knots and links, called homogeneously adequate knots and links, in terms of their diagrams. To do so, we use the decomposition of these links into ideal polyhedra, developed by Futer, Kalfagianni, and Purcell. We identify essential product disks in these polyhedra.