Do markets move in the shape of a torus, which is at the heart of the constructal principle more frequently than chance, and is it predictive?

When you say “torus” I think “circle times circle”. (Referring to the surface of the torus, not a solid torus.)

The surface of a sphere, by contrast, is not circle times circle. (The standard physical models are: two angular measurements in a TIE fighter, versus lat/long measurements on the Globe. (Think about the poles and notice that lat is 180 degrees, not 360.))

From an external point of view the surface of a torus is a 2-dimensional curved surface with one hole in it.

By “markets” I assume you mean agreed prices over time (for some contract? for some index/composite?). Prices are (nonnegative) scalars, not surfaces, so somehow we need to make the prices “live” on that surface, i.e., map from possible price space to the torus’ surface.

In that context — what would genus 1 (number of holes==1) mean?
A related idea, which is not speculative at all, is to use “projective spaces” in portfolio design. This is what is going on when people talk about purchasing a security for $0.97 and selling it for $1.00.