The eta-invariant of variation structures. I (Q1910694)

Let \(f_1 : (\mathbb{C}^{n + 1}, 0) \to (\mathbb{C}, 0)\) be an analytic map germ with one-dimensional singular locus. Choose a germ \(f_2\) such that \((f_1, f_2)\) defines an isolated complete intersection singularity. It is proved that for sufficiently large \(q\) the difference \(\sigma (f_1 + f^q_2 - \sigma (f_1)\), where \(\sigma (f)\) denotes the signature of the Milnor fibre of the germ \(f\), can be expressed in terms of so-called eta-invariants depending on the monodromy representation and the variation map.