Embeddings in the 3/4 range

We give a complete obstruction to turning an immersion f:Mm→Rn into an embedding when 3n⩾4m+5. It is a secondary obstruction, and exists only when the primary obstruction, due to André Haefliger, vanishes. The obstruction lives in a twisted cobordism group, and its vanishing implies the existence of an embedding in the regular homotopy class of f in the range indicated. We use Tom Goodwillie's calculus of functors, following Michael Weiss, to help organize and prove the result.