Branched covers of contact manifolds

Branched covers;Contact geometry

Casey, Meredith Perrie ; Etnyre, John Mathematics Kazez, Will Margalit, Dan Belegradek, Igor Le, Thang ; Etnyre, John

University:Georgia Institute of Technology

Department:Mathematics

关键词: Branched covers;    Contact geometry;   

Others  :  https://smartech.gatech.edu/bitstream/1853/50313/1/CASEY-DISSERTATION-2013.pdf

美国|英语

来源: SMARTech Repository

【 摘 要 】

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.