University of Sydney Algebra Seminar
Colin Reid (University of Newcastle)
Friday 25 Sep, 12-1pm, Place: Carslaw 375
Normal subgroup structure in Polish groups
I will present joint work with Phillip Wesolek (UCLouvain, Belgium).
The isomorphism theorems of group theory have deficiencies in the setting of topological groups, because an injective continuous group homomorphism is not in general a closed map. This is an obstacle to developing a well-behaved theory of series of closed normal subgroups in topological groups. We develop some theory to overcome these complications in the context of Polish groups, that is, topological groups in which the topology is separable and completely metrizable. The key observation in the Polish context is that given an injective, continuous homomorphism