To a germ with one-dimensional singular locus one associates series of isolated singularities , where l is a general linear function and . We prove an attaching result of Iomdin-Lê type which compares the homotopy types of the Milnor fibres of and f. This is a refinement of the Iomdin-Lê theorem in the general setting of a singular underlying space.
We survey some recent results concerning the behavior of the contact structure defined on the boundary of a complex isolated hypersurface singularity or on the boundary at infinity of a complex polynomial.
We define open book structures with singular bindings. Starting with an extension of Milnor’s results on local fibrations for germs with nonisolated singularity, we find classes of genuine real analytic mappings which yield such open book structures.
We prove a sufficient condition for the Jacobian problem in the setting of real, complex and mixed polynomial mappings. This follows from the study of the bifurcation locus of a mapping subject to a new Newton non-degeneracy condition.
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