Poltical Ideology

What is the fundamental group of political ideology. Are all loops null homotopic or are there certain loops that are permanently orthogonal?

On a torus there are two distinct classes of loops that can't be shrunk to a point. They are always, in a sense, perpendicular.

On a sphere, any loop can be moved around on the surface and transformed into any other loop, and all loops can be shrunk down to a point.

I'm not sure, but I think about it a lot, and anyways I am a point not a loop so I move around. I like to take a peak at different homotopy classes. But not everyone can afford the 10,000 foot view, I suppose.