Sensory stimuli evoke activity in a population of neurons in cortex. In topographically organized networks, activated neurons with similar receptive fields occur within a relatively confined area, suggesting that the spatial distribution and firing dynamics of the neuron population contribute to processing of sensory information. However, inherent variability in neuronal firing, makes it difficult to determine which neurons encode signal and which represent noise. Here, we use simplicial complexes to identify functionally relevant neurons whose activities are likely to be propagated and to distinguish between multiple populations activated during complex stimuli. Moreover, preliminary analyses suggest that changes in the extent and magnitude of network activity can be described abstractly as the movement of points on the surface of a torus.