Introduction to Branched Covers

Geometry Topology Student Seminar
Wednesday, October 26, 2011 - 14:00
1 hour (actually 50 minutes)
Skiles 005
Georgia Tech
The main purpose of this talk is to better understand how to use branched covers to construct 3-manifolds.  We will start with branched covers of 2-manifolds, carefully working through examples and learning the technology.  Using these methods in combination with open book decompositions we will show how to construct 3-manifolds by branching over link and knots in S^{3}.  Particular emphasis will be placed on using the map to get a "coloring" of the branched locus and how this combinatorial data is useful both for explicit constructions and for the general theory.