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 Mat. Zametki, 1996, Volume 60, Issue 2, Pages 206–224 (Mi mz1820)

Rudolph diagrams and an analytic realization of the Vitushkin covering

S. Yu. Orevkov

Scientific Research Institute for System Studies of RAS

Abstract: 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.

DOI: https://doi.org/10.4213/mzm1820

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English version:
Mathematical Notes, 1996, 60:2, 153–164

Bibliographic databases:

UDC: 515.16

Citation: S. Yu. Orevkov, “Rudolph diagrams and an analytic realization of the Vitushkin covering”, Mat. Zametki, 60:2 (1996), 206–224; Math. Notes, 60:2 (1996), 153–164

Citation in format AMSBIB
\Bibitem{Ore96} \by S.~Yu.~Orevkov \paper Rudolph diagrams and an analytic realization of the Vitushkin covering \jour Mat. Zametki \yr 1996 \vol 60 \issue 2 \pages 206--224 \mathnet{http://mi.mathnet.ru/mz1820} \crossref{https://doi.org/10.4213/mzm1820} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1429122} \zmath{https://zbmath.org/?q=an:0897.57002} \transl \jour Math. Notes \yr 1996 \vol 60 \issue 2 \pages 153--164 \crossref{https://doi.org/10.1007/BF02305179} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1996WE97100023} 

• http://mi.mathnet.ru/eng/mz1820
• https://doi.org/10.4213/mzm1820
• http://mi.mathnet.ru/eng/mz/v60/i2/p206

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. A. G. Vitushkin, “On the homology of a ramified covering over $\mathbb C^2$”, Math. Notes, 64:6 (1998), 726–731
2. A. G. Vitushkin, “A criterion for the representability of a chain of $\sigma$-processes by a composition of triangular chains”, Math. Notes, 65:5 (1999), 539–547
3. G. V. Egorov, “Example of a Five-Sheeted Exotic Covering over $\mathbb C^2$”, Math. Notes, 71:4 (2002), 486–499
4. A. S. Bystrikov, “On the Equivalence of Elementary Chains of Monoidal Transformations of the Projective Plane”, Math. Notes, 73:5 (2003), 611–617
5. G. V. Egorov, “Branched Coverings over $\mathbb C^2$ and the Jacobian Conjecture”, Math. Notes, 76:2 (2004), 161–169
6. Zoladek H., “An application of Newton-Puiseux charts to the Jacobian problem”, Topology, 47:6 (2008), 431–469
7. Feller P., “Optimal cobordisms between torus knots”, Commun. Anal. Geom., 24:5 (2016), 993–1025
8. Hayden K., “Cross-Sections of Unknotted Ribbon Disks and Algebraic Curves”, Compos. Math., 155:2 (2019), 413–423
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