Farey Recursion and Hyperbolic Dehn Filling

Author

Jose Ebenezer MartinezFollow

Year of Award

2024

Document Type

Dissertation

Degree Type

Doctor of Philosophy (PhD)

Degree Name

Mathematics

Department or School/College

Mathematical Sciences

Committee Chair

Eric Chesebro

Commitee Members

Kelly McKinnie, Karel Stroethoff, Elizabeth Gillaspy, David Macaluso

Keywords

geometric topology, hyperbolic geometry, 3-manifolds, layered solid torus

Subject Categories

Geometry and Topology

Abstract

In this work, we present a solution to William Thurston's edge gluing equations for Dehn fillings of hyperbolic 3-manifolds. This is done for triangulations that involve the layered solid torus. Our approach uses Farey recursive functions, and we present a Farey recursive function that provides a solution to the gluing equations for any hyperbolic Dehn filling admitting a triangulation by the layered solid torus. We provide examples that demonstrate our solution for multiple 3-manifolds, and study the roots of the corresponding Farey recursive polynomials. As an additional application of our solution, we provide a formula for the complex length of the core geodesic of the layered solid torus.

Recommended Citation

Martinez, Jose Ebenezer, "Farey Recursion and Hyperbolic Dehn Filling" (2024). Graduate Student Theses, Dissertations, & Professional Papers. 12307.
https://scholarworks.umt.edu/etd/12307