Dissertations, Theses, and Capstone Projects
Date of Degree
9-2019
Document Type
Dissertation
Degree Name
Ph.D.
Program
Mathematics
Advisor
Abhijit Champanerkar
Advisor
Dennis Sullivan
Committee Members
Ilya Kofman
Abstract
The Geometrization Theorem for 3-manifolds states that every closed orientable 3-manifold can be cut along spheres and tori into pieces which have a geometric structure modeled on one of the eight, 3-dimensional geometries. In joint work with Dennis Sullivan, we combine the different geometries on the toroidal ends of 3-manifolds to describe a uniform geometric structure for all oriented closed prime 3-manifolds. Hyperbolic structures on links in the thickened torus and their geometric properties have been of great interest recently. We discuss geometric properties of augmented and fully augmented links in the thickened torus. We show how sequences of fully augmented links in the 3-sphere which diagrammatically converge to a biperiodic fully augmented link have interesting asymptotic volume growth.
Recommended Citation
Kwon, Alice, "Geometric Properties of Closed Three Manifolds and Hyperbolic Links" (2019). CUNY Academic Works.
https://academicworks.cuny.edu/gc_etds/3369