Closed manifold surgery obstructions and the Oozing Conjecture

We complete the description of surgery obstructions up to homotopy equivalence for closed oriented manifolds with finite fundamental group. New examples are presented of non-trivial obstructions for Arf invariant product formulas in codimensions $\ge 4$, which give counterexamples to the well-known ‘‘Oozing Conjecture’’ from the 1980’s.