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Izv. Akad. Nauk SSSR Ser. Mat., 1949, Volume 13, Issue 5, Pages 389–402 (Mi izv3204)  

This article is cited in 20 scientific papers (total in 21 papers)

On the topology of real algebraic surfaces

I. G. Petrovskii, O. A. Oleinik


Full text: PDF file (1409 kB)

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Received: 12.05.1949

Citation: I. G. Petrovskii, O. A. Oleinik, “On the topology of real algebraic surfaces”, Izv. Akad. Nauk SSSR Ser. Mat., 13:5 (1949), 389–402

Citation in format AMSBIB
\Bibitem{PetOle49}
\by I.~G.~Petrovskii, O.~A.~Oleinik
\paper On the topology of real algebraic surfaces
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1949
\vol 13
\issue 5
\pages 389--402
\mathnet{http://mi.mathnet.ru/izv3204}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=34600}
\zmath{https://zbmath.org/?q=an:0035.10204}


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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. E. P. Dolzhenko, “Nekotorye metricheskie svoistva algebraicheskikh giperpoverkhnostei”, Izv. AN SSSR. Ser. matem., 27:2 (1963), 241–252  mathnet  mathscinet  zmath
    2. V. M. Kharlamov, “The maximal number of components of a fourth degree surface in $\mathbb{RP}^3$”, Funct. Anal. Appl., 6:4 (1972), 345–346  mathnet  crossref  mathscinet  zmath
    3. D. A. Gudkov, “The topology of real projective algebraic varieties”, Russian Math. Surveys, 29:4 (1974), 1–79  mathnet  crossref  mathscinet  zmath
    4. V. I. Zvonilov, “Kharlamov's inequalities and Petrovskii–Oleinik inequalities”, Funct. Anal. Appl., 9:2 (1975), 152–153  mathnet  crossref  mathscinet  zmath
    5. V. M. Kharlamov, “A generalized Petrovskii inequality. II”, Funct. Anal. Appl., 9:3 (1975), 266–268  mathnet  crossref  mathscinet  zmath
    6. V. A. Krasnov, “A generalized Petrovsky inequality for odd-degree curves”, Funct. Anal. Appl., 10:2 (1976), 116–121  mathnet  crossref  mathscinet  zmath
    7. A. G. Khovanskii, “Newton polyhedra and the Euler–Jacobi formula”, Russian Math. Surveys, 33:6 (1978), 237–238  mathnet  crossref  mathscinet  zmath
    8. V. I. Arnol'd, “Index of a singular point of a vector field, the Petrovskii–Oleinik inequality, and mixed hodge structures”, Funct. Anal. Appl., 12:1 (1978), 1–12  mathnet  crossref  mathscinet  zmath
    9. V. V. Nikulin, “Integral symmetric bilinear forms and some of their applications”, Math. USSR-Izv., 14:1 (1980), 103–167  mathnet  crossref  mathscinet  zmath  isi
    10. A. G. Khovanskii, “Index of a polynomial field”, Funct. Anal. Appl., 13:1 (1979), 38–45  mathnet  crossref  mathscinet  zmath
    11. O. Ya. Viro, “Construction of $M$-surfaces”, Funct. Anal. Appl., 13:3 (1979), 212–213  mathnet  crossref  mathscinet  zmath
    12. E. A. Sevast'yanov, “The degree of rational approximation of functions and their differentiability”, Math. USSR-Izv., 17:3 (1981), 595–600  mathnet  crossref  mathscinet  zmath  isi
    13. V. V. Nikulin, “Involutions of integral quadratic forms and their applications to real algebraic geometry”, Math. USSR-Izv., 22:1 (1984), 99–172  mathnet  crossref  mathscinet  zmath
    14. V. N. Karpushkin, “Precise order bounds for the number of components of the complement of the zeros of harmonic polynomials”, Funct. Anal. Appl., 19:4 (1985), 295–299  mathnet  crossref  mathscinet  zmath  isi
    15. O. Ya. Viro, “Progress in the topology of real algebraic varieties over the last six years”, Russian Math. Surveys, 41:3 (1986), 55–82  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    16. V. N. Karpushkin, “Bounds for the Betti numbers of a level surface of a harmonic polynomial”, Funct. Anal. Appl., 26:4 (1992), 300–302  mathnet  crossref  mathscinet  zmath  isi
    17. V. N. Karpushkin, “Bounds for Homology Groups of Some Manifolds”, Funct. Anal. Appl., 27:2 (1993), 146–147  mathnet  crossref  mathscinet  zmath  isi
    18. V. N. Karpushkin, “The number of components of complements to level surfaces of partially harmonic polynomials”, Math. Notes, 62:6 (1997), 697–700  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    19. A. I. Degtyarev, V. M. Kharlamov, “Topological properties of real algebraic varieties: du coté de chez Rokhlin”, Russian Math. Surveys, 55:4 (2000), 735–814  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    20. V. I. Arnol'd, “I. G. Petrovskii, Hilbert's topological problems, and modern mathematics”, Russian Math. Surveys, 57:4 (2002), 833–845  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    21. A. G. Vitushkin, “On Hilbert's thirteenth problem and related questions”, Russian Math. Surveys, 59:1 (2004), 11–25  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
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