Neurogeometry of neural functional architectures

The term “neurogeometry” denotes the geometry of the functional architecture of visual areas. The paper reviews some elements of the neurogeometry of the functional architecture of the first visual area V1 and explains why contact geometry, sub-Riemannian geometry, and noncommutative harmonic analysis are brought in as natural tools. It emphasizes the fact that these geometries are radically different from Riemannian geometries.