Versions Revisited
In the topological category the surgery obstruction map can be made into a homomorphism. This is achieved by putting an alternative abelian group structure on the normal invariants as described here. Moreover, the surgery exact sequence can be identified with the algebraic surgery exact sequence of Ranicki which is an exact sequence of abelian groups by definition. This gives the structure set the structure of an abelian group. Note, however, that there is to this date no satisfactory geometric description of this abelian group structure.
Read more about this topic: Surgery Exact Sequence
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