An Intrinsic Arf Invariant on a Link and its Surface-Link Analogue

We define a modulo one rational number invariant of order up to 2 as the Arf invariant of the -hyperbolic quadratic function of every infinite cyclic covering of every (possibly non-orientable) compact 3-manifold, and analogously a modulo one rational number invariant of order up to 4 as an invariant of the /-quadratic function of every infinite cyclic covering of every compact oriented 4-manifold. Typically the invariants become an invariant of an arbitrary oriented link in and an invariant of an arbitrary oriented surface-link in