Geodesic
On the Continuability of Multivalued Analytic Functions to an Analytic Subset
Funkcionalʹnyj analiz i ego priloženiâ, Tome 35 (2001) no. 1, pp. 62-73

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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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     author = {A. G. Khovanskii},
     title = {On the {Continuability} of {Multivalued} {Analytic} {Functions} to an {Analytic} {Subset}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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     number = {1},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2001_35_1_a5/}
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A. G. Khovanskii. On the Continuability of Multivalued Analytic Functions to an Analytic Subset. Funkcionalʹnyj analiz i ego priloženiâ, Tome 35 (2001) no. 1, pp. 62-73. http://geodesic.mathdoc.fr/item/FAA_2001_35_1_a5/