How much are vector bundles like complexity classes?

Complexity classes can be thought of as bundles of programs over the space of problems. We have better tools for classifying bundles when the objects have more structure (e.g., fiber bundles, vector bundles, etc.). Is there a model of computation where complexity classes are vector bundles? Can we separate the analog of \(\mathrm{P}\) from the analog of \(\mathrm{NP}\) there?