Capabilities for collecting and storing data on mobile objects have increased dramatically over the past few decades. A persistent difficulty is summarizing large collections of mobile objects. This paper develops methods for extracting and analyzing hotspots or locations with relatively high levels of mobility activity. We use kernel density estimation (KDE) to convert a large collection of mobile objects into a smooth, continuous surface. We then develop a topological algorithm to extract critical geometric features of the surface; these include critical points (peaks, pits and passes) and critical lines (ridgelines and course-lines). We connect the peaks and corresponding ridgelines to produce a surface network that summarizes the topological structure of the surface. We apply graph theoretic indices to analytically characterize the surface and its changes over time. To illustrate our approach, we apply the techniques to taxi cab data collected in Shanghai, China. We find increases in the complexity of the hotspot spatial distribution during normal activity hours in the late morning, afternoon and evening and a spike in the connectivity of the hotspot spatial distribution in the morning as taxis concentrate on servicing travel to work. These results match with scientific and anecdotal knowledge about human activity patterns in the study area.