By analogy with knot theory, complex hypersurfaces can be studied via Alexander-type invariants of their complements. I will discuss old and new results concerning rigidity properties of such invariants, including (twisted) Alexander polynomials, L^2-betti numbers, and Novikov homology. In relation to an old question of Serre, such rigidity results impose severe restrictions on the type of groups which can be realized as fundamental groups of complex hypersurface complements.
Geometry-Topology Seminar
Tuesday, February 14, 2017 - 4:30pm
Laurentiu Maxim
University of Wisconsin