Rudolph diagrams and an analytic realization of the Vitushkin covering
Matematičeskie zametki, Tome 60 (1996) no. 2, pp. 206-224.

Voir la notice de l'article provenant de la source Math-Net.Ru

An example of a three-sheeted covering over the ball in $\mathbb C^2$ is constructed. The covering is the union of a four-dimensional ball with an analytic disk. The projection of the ball is a local homeomorphism ramified along the disk, whose projection is a part of an algebraic curve.
@article{MZM_1996_60_2_a4,
     author = {S. Yu. Orevkov},
     title = {Rudolph diagrams and an analytic realization of the {Vitushkin} covering},
     journal = {Matemati\v{c}eskie zametki},
     pages = {206--224},
     publisher = {mathdoc},
     volume = {60},
     number = {2},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1996_60_2_a4/}
}
TY  - JOUR
AU  - S. Yu. Orevkov
TI  - Rudolph diagrams and an analytic realization of the Vitushkin covering
JO  - Matematičeskie zametki
PY  - 1996
SP  - 206
EP  - 224
VL  - 60
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_1996_60_2_a4/
LA  - ru
ID  - MZM_1996_60_2_a4
ER  - 
%0 Journal Article
%A S. Yu. Orevkov
%T Rudolph diagrams and an analytic realization of the Vitushkin covering
%J Matematičeskie zametki
%D 1996
%P 206-224
%V 60
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_1996_60_2_a4/
%G ru
%F MZM_1996_60_2_a4
S. Yu. Orevkov. Rudolph diagrams and an analytic realization of the Vitushkin covering. Matematičeskie zametki, Tome 60 (1996) no. 2, pp. 206-224. http://geodesic.mathdoc.fr/item/MZM_1996_60_2_a4/

[1] Vitushkin A. G., “Nekotorye primery v svyazi s zadachei polinomialnykh preobrazovanii $\mathbb C^n$”, Izv. AN SSSR. Ser. matem., 35 (1971), 269–279 | Zbl

[2] Vitushkin A. G., “On polynomial transformation of $\mathbb C^n$”, Manifolds, Tokyo Univ. Press, Tokyo, 1975, 415–417 | Zbl

[3] Bass H., Connell E. H., Wright D., “The Jacobian Conjecture: reduction of degree and formal expansion of the inverse”, Bull. Amer. Math. Soc., 7 (1982), 287–330 | DOI | Zbl

[4] Eliashberg Ya., “Filling by holomorphic discs and its applications”, Geometry of low dimensional manifolds, London Math. Soc. Lect. Notes, 151, London, 1991, 45–67

[5] Rudolph L., “Algebraic functions and closed braids”, Topology, 22 (1983), 191–202 | DOI | Zbl

[6] Orevkov S. Yu., “Fundamentalnaya gruppa dopolneniya ploskoi algebraicheskoi krivoi”, Matem. sb., 137(179):2 (1988), 260–270

[7] Birman J. S., Hilden H. M., “Heegaard splittings of branched covering of $S^3$”, Trans. Amer. Math. Soc., 213 (1975), 315–352 | DOI | Zbl

[8] Orevkov S. Yu., “Kommutant fundamentalnoi gruppy dopolneniya ploskoi algebraicheskoi krivoi”, UMN, 45:1 (1990), 183–184 | Zbl

[9] Foks R., “Kratkii ekskurs v teoriyu uzlov”, Vvedenie v teoriyu uzlov, eds. R. Krouell, R. Foks, Mir, M., 1967

[10] Magnus V., Karrass A., Soliter D., Kombinatornaya teoriya grupp, Nauka, M., 1974 | Zbl

[11] Orevkov S. Yu., “O trekhlistnykh polinomialnykh otobrazheniyakh $\mathbb C^2$”, Izv. AN SSSR. Ser. matem., 50:6 (1986), 1231–1240 | Zbl