Four dimensional hyperbolic link complements via Kirby calculus

Thesis

The primary aim of this thesis is to construct explicit examples of four dimensional hyperbolic link complements. Using the theory of Kirby diagrams and Kirby calculus we set up a general framework that one can use to attack such a problem. We use this framework to construct explicit examples in a smooth standard S⁴ and a smooth standard S² x S². We then characterise which homeomorphism types of smooth simply connected closed 4-manifolds can admit a hyperbolic link complement, along the way giving constructions of explicit examples.

Authors: Saratchandran, H

• Publication date: 2015
• DOI: 10.5287/ora-6qv9ar41j
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: Oxford University, UK
• Language: English
• Keywords: hyperbolic geometry
• Subjects: Geometry