Imaging inhomogenous Hall states in transport

The quantum Hall state is the archetypical example of topological matter. Its topology is characterized in terms of Chern numbers, which are defined in momentum space. Along similar lines, topology is generally said to be non-local. However, that does not mean that momentum space is a prerequisite for topological physics. In this talk, I will present recent results on inhomogenous quantum Hall systems, and discuss how to think of them in terms of a spatially variying topological character. I will close by describing how their spatially variying topological character can be mapped in transport experiments.