In differential geometry, position is a point in a manifold, velocity is a vector in the tangent bundle, and acceleration is a quantity in the double tangent bundle (or the tangent bundle if a connection is used). These characterize the derivatives of position, but what about its “integrals”? Absement is an obscure quantity related to how far an object is displaced for how much time. As it’s (kind of) the integral of position, where would this live? Heuristically, it should live in the “inverse tangent bundle”, $T^{-1}M$, but that doesn’t exist and I don’t even know what it would be. My second guess is that it would live in the cotangent bundle, but I can’t be certain of that either.
How would absement be characterized in terms of differential geometry?