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 S<sup>4</sup> and a smooth standard S<sup>2</sup> x S<sup>2</sup>. 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.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:647681 |
| Date | January 2015 |
| Creators | Saratchandran, Hemanth |
| Contributors | Lackenby, Marc |
| Publisher | University of Oxford |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://ora.ox.ac.uk/objects/uuid:ba72ee75-c22f-4800-a38c-76e5cf411ad9 |
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