# Stably parallelizable iff framable in large codimension

From Diffgeom

## Statement

Suppose is a differential manifold. Then, the following are equivalent:

- is a stably parallelizable manifold i.e. its tangent bundle is a stably trivial vector bundle
- There exists a manifold such that can be embedded as a framable submanifold of
- There exists a manifold of dimension at most , such that can be embedded as a framable submanifold of