Signature of the Milnor fiber of parametrized surfaces
R. Giménez Conejero, Gergő Pintér
Source abstract
Abstract We compute the signature of the Milnor fiber of certain type of nonisolated complex surface singularities, namely, images of finitely determined holomorphic germs. An explicit formula is given in algebraic terms. As a corollary we show that the signature of the Milnor fiber is a topological invariant for these singularities. The proof combines complex analytic and smooth topological techniques. The main tools are Thom–Mather theory of map germs and the Ekholm–Szűcs–Takase–Saeki formula for immersions. We give a table with many examples for which the signature is computed using our formula.
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