Let G be a finite group and let f : X --> Y be a degree 1, G-framed map such that X and Y are simply connected, closed, oriented, smooth manifolds of dimension n = 2k greater than or equal to 6 and such that the dimension of the singular set of the G-space X is at most k. In the previous article, assuming f is k-connected, we defined the G-equivariant surgery obstruction sigma (f) in a certain abelian group. There it was shown that if sigma (f) = 0 then f is G-framed cobordant to a homotopy equivalence f' : X' --> Y. In the present article, we prove that the obstruction sigma (f) is a G-framed cobordism invariant. Consequently, the G-surgery obstruction sigma (f) is uniquely associated to f : X --> Y above even if it is not k-connected. [References: 10]
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