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Cortical Functional architectures as contact and sub-Riemannian geometry
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