The Cartesian product structure and 𝐶^{∞} equivalances of singularities

Ephraim, Robert

doi:10.1090/S0002-9947-1976-0422676-6

The Cartesian product structure and $C^{\infty }$ equivalances of singularities
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Trans. Amer. Math. Soc. 224 (1976), 299-311 Request permission

Abstract:

In this paper the cartesian product structure of complex analytic singularities is studied. A singularity is called indecomposable if it cannot be written as the cartesian product of two singularities of lower dimension. It is shown that there is an essentially unique way to write any reduced irreducible singularity as a cartesian product of indecomposable singularities. This result is applied to give an explicit description of the set of reduced irreducible complex singularities having a given underlying real analytic structure.

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