Riemannian Topological Analysis of Neuronal Activity

Cerebral dynamics emerge from the brain’s substrate due to the anatomical patterns of its physical connections, which we know are not a fixed structure but are subject to temporal and local modifications. This circumstance makes it possible for a more or less fixed number of neurons to generate a range of complex networks. By studying the topological space associated with these physical connections and their geometric dynamics, we can use Differential Geometry to study the foundations of the brain’s connectome.