Local Topology of Analytic Spaces

Let M be a subset of CN defined as the common zero set of some holomorphic functions. What can one say about the local structure of M? Each point p ! M has an open neighborhood that is a cone over an (odd real dimensional) topological space called the link of p. If p is a smooth point of complex dimension n, the link is a sphere of real imension 2n−1.

Our main interest is to understand the most complicated links. The general answer is not known but we show how to construct examples where the fundamental group of a link  is nearly arbitrary. Joint work with Misha Kapovich.