notion is the concept of a π-manifold. A smooth manifold is called a π-manifold if, when embedded in a high dimensional euclidean space, its normal bundle is trivial. In particular, every parallelizable manifold is a π-manifold. See also Chart (topology) Differentiable manifold Frame bundle Kervaire invariant Orthonormal frame bundle Principal bundle Connection (mathematics) G-structure Notes References Differential topology Fiber bundles Manifolds Vector bundles