The codimension Arf invariant vanishing conjecture

For a closed oriented or non-orientable manifold product with an Arf invariant normal map, the resulting surgery obstruction modulo the ordinary Arf–Kervaire invariant is called a codimension $k$ Arf invariant. Codimension Arf invariant vanishing conjecture. The codimension $k$ Arf invariants are trivial for $k\geq 4$. This was a well-known conjecture from the 1980s; the paper disproves the associated oozing conjecture by exhibiting non-trivial examples in codimensions $k=2^l$ for $l\text{≥}2$.