English

Cortical Functional architectures as contact and sub-Riemannian geometry

Neurons and Cognition 2023-10-26 v1 Differential Geometry

Abstract

In a joint paper, Jean Petitot together with the authors of the present paper described the functional geometry of the visual cortex as the symplectization of a contact form to describe the family of cells sensitive to position, orientation and scale. In the present paper, as a "homage" to the enormous contribution of Jean Petitot to neurogeometry, we will extend this approach to more complex functional architectures built as a sequence of contactization or a symplectization process, able to extend the dimension of the space. We will also outline a few examples where a sub-Riemannian lifting is needed.

Keywords

Cite

@article{arxiv.2310.16056,
  title  = {Cortical Functional architectures as contact and sub-Riemannian geometry},
  author = {Giovanna Citti and Alessandro Sarti},
  journal= {arXiv preprint arXiv:2310.16056},
  year   = {2023}
}