Abstract:

In many respects discrete and open mappings are generalizations of PL branched covers. For example, by Väisälä's theorem, the singular set, where the mapping fails to be a local homeomorphism, has codimension at least 2. Although such generalized branched covers have been of interest -- for example in geometric analysis -- from the late 1960's, there are very few results on the topology of the singular set in higher dimensions. In this talk I will discuss a connection of the local monodromy of the map to the local dimension of the singular set. This is joint work with Martina Aaltonen.