In mathematics, the tautological bundle is a vector bundle occurring over a Grassmannian in a natural tautological way: for a Grassmannian of k {\displaystyle k} -dimensional subspaces of V {\displaystyle V}, given a point in the Grassmannian corresponding to a k {\displaystyle k} -dimensional vector subspace W ⊆ V {\displaystyle W\subseteq V}, the fiber over W {\displaystyle W} is the subspace W {\displaystyle W} itself. Wikipedia