The Exactness
Recall that the surgery structure set is only a pointed set and that the surgery obstruction map might not be a homomorphism. Hence it is necessary to explain what is meant when talking about the "exact sequence". So the surgery exact sequence is an exact sequence in the following sense:
For a normal invariant we have if and only if . For two manifold structures we have if and only if there exists such that . For an element we have if and only if .
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