Abstract
We give a complete obstruction to turning an immersion f : M m → R n into an embedding when 3 n ⩾ 4 m + 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.
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