A mathematical model of the motor cortex

In this work we present a geometric model of motor cortex that generalizes an already existing model of visual cortex. The thesis opens by recalling the notions of fiber bundles, principal bundles, Lie groups and sub-Riemannian geometry. In particular, we enunciate Chow’s theorem which ensures that if the Hörmander condition holds, the space connectivity property is satisfied. Then we recall the visual cortex model proposed by Citti-Sarti, which describes the set of simple cells as a Lie group with sub-Riemannian metric. The original part of the thesis is the extension to the motor cortex. Based on neural data, collected by Georgopoulos, we study the set of motor cortical cells and we describe them as a principal bundle. The fiber contains the movement direction and shapes the hypercolumnar structure measured. Finally we determine the intrinsic coordinates of the motor cortex, studying the cellular response to the motor impulse.