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To a germ f : (C, 0)→ (C, 0) with one-dimensional singular locus one associates series of isolated singularities fN := f + l N , where l is a general linear function and N ∈ N. We prove an attaching result of Iomdin-Lê type which compares the homotopy types of the Milnor fibres of fN and f . This is a refinement of the Iomdin-Lê theorem in the general setting of a singular underlying space.

A supplement to the Iomdin-Lê theorem for singularities with one-dimensional singular locus