We will discuss what is known about the construction of contact structures via branched covers, emphasizing the search for universal transverse knots. Recall that a topological knot is called universal if all 3-manifold can be obtained as a cover of the 3-sphere branched over that knot. Analogously one can ask if there is a transverse knot in the standard contact structure on S³ from which all contact 3-manifold can be obtained as a branched cover over this transverse knot. It is not known if such a transverse knot exists.
Identifer | oai:union.ndltd.org:GATECH/oai:smartech.gatech.edu:1853/50313 |
Date | 13 January 2014 |
Creators | Casey, Meredith Perrie |
Contributors | Etnyre, John |
Publisher | Georgia Institute of Technology |
Source Sets | Georgia Tech Electronic Thesis and Dissertation Archive |
Language | en_US |
Detected Language | English |
Type | Dissertation |
Format | application/pdf |
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