I will discuss some of the interplay between complex algebraic geometry and low-dimensional topology, as it occurs when studying the fundamental groups of quasi-projective manifolds and 3-manifolds, or the Milnor fibrations of arrangements of complex planes. The bridge between the two settings is provided by the Alexander polynomial and its various generalizations.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/5019