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}
}