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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

The Cartesian product structure and $ C\sp{\infty }$ equivalances of singularities


Author: Robert Ephraim
Journal: Trans. Amer. Math. Soc. 224 (1976), 299-311
MSC: Primary 32C40; Secondary 32B10
MathSciNet review: 0422676
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1976-0422676-6
PII: S 0002-9947(1976)0422676-6
Keywords: Reduced singularity, irreducible singularity, cartesian product, underlying real analytic structure, complexification, complex conjugate, real analytic isomorphism, $ {C^\infty }$ isomorphism
Article copyright: © Copyright 1976 American Mathematical Society