 The Arf invariant is analogous to the signature of a manifold, which is defined for 4"k"-dimensional manifolds (doubly even-dimensional); this 4-fold periodicity corresponds to the 4-fold periodicity of L-theory.The Arf invariant can also be defined more generally for certain 2"k"-dimensional manifolds.The Arf invariant is defined for a quadratic form "q" over a field "K" of characteristic 2 such that "q" is nonsingular, in the sense that the associated bilinear form formula_1 is nondegenerate.