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On the Continuability of Multivalued Analytic Functions to an Analytic Subset

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Functional Analysis and Its Applications Aims and scope

Abstract

In the paper, it is shown that a germ of a many-valued analytic function can be continued analytically along the branching set at least until the topology of this set is changed. This result is needed to construct the many-dimensional topological version of Galois theory. The proof heavily uses Whitney's stratification.

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References

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Authors and Affiliations

  1. Institute for System Analysis, Russian Academy of Sciences, Russia

    A. G. Khovanskii

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  1. A. G. Khovanskii
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Khovanskii, A.G. On the Continuability of Multivalued Analytic Functions to an Analytic Subset. Functional Analysis and Its Applications 35, 52–60 (2001). https://doi.org/10.1023/A:1004124600978

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  • DOI: https://doi.org/10.1023/A:1004124600978

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