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Izv. RAN. Ser. Mat., 1995, Volume 59, Issue 5, Pages 19–40 (Mi izv39)  

This article is cited in 6 scientific papers (total in 6 papers)

A description of characteristic classes of real submanifolds in complex manifolds via RC-singularities

A. V. Domrin


Abstract: Let $X$ be a complex manifold, $M\subset X$ a (closed, orient) real submanifold, and $S\subset M$ the set of RC-singular points of $M$. We study the connection between the global topological characteristics of $S$ and the topology of $M$ and $X$. For the case of discrete $S$ we introduce a notion of an isolate RC-singular point and obtain a formula expressing the sun of indices over $S$ in terms of the Chern classes of $X$ and the Pontryagin classes of $M$ and of the normal bundle to $M$ in $X$ (Theorem 1). In the general case we express the Poincare dual to $S$ (Theorem 2) and the Poincare duals to some cycles carried by subsets of $S$ (Theorem 3) in a similar way.

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English version:
Izvestiya: Mathematics, 1995, 59:5, 899–918

Bibliographic databases:

MSC: 57R20
Received: 12.05.1995

Citation: A. V. Domrin, “A description of characteristic classes of real submanifolds in complex manifolds via RC-singularities”, Izv. RAN. Ser. Mat., 59:5 (1995), 19–40; Izv. Math., 59:5 (1995), 899–918

Citation in format AMSBIB
\Bibitem{Dom95}
\by A.~V.~Domrin
\paper A~description of characteristic classes of real submanifolds in complex manifolds via
RC-singularities
\jour Izv. RAN. Ser. Mat.
\yr 1995
\vol 59
\issue 5
\pages 19--40
\mathnet{http://mi.mathnet.ru/izv39}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1360632}
\zmath{https://zbmath.org/?q=an:0877.57011}
\transl
\jour Izv. Math.
\yr 1995
\vol 59
\issue 5
\pages 899--918
\crossref{https://doi.org/10.1070/IM1995v059n05ABEH000039}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995UH54100002}


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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. Adam Coffman, “Analytic stability of the CR cross-cap”, Pacific J Math, 226:2 (2006), 221  crossref  mathscinet  zmath  isi
    2. V. K. Beloshapka, V. V. Ezhov, G. Schmalz, “Holomorphic classification of four-dimensional surfaces in $\mathbb C^3$”, Izv. Math., 72:3 (2008), 413–427  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. Stefan Nemirovski, “Lagrangian Klein Bottles in
      $${\mathbb{R}^{2n}}$$
      ”, GAFA Geom funct anal, 2009  crossref  mathscinet  isi
    4. Coffman A., “Cr Singularities of Real Fourfolds in C-3”, Ill. J. Math., 53:3 (2009), 939–981  mathscinet  zmath  isi
    5. Elgindi A.M., “A topological obstruction to the removal of a degenerate complex tangent and some related homotopy and homology groups”, Int. J. Math., 26:5 (2015), 1550025  crossref  mathscinet  zmath  isi  scopus
    6. Elgindi A.M., “Totally Real Perturbations and Nondegenerate Embeddings of S-3”, N. Y. J. Math., 21 (2015), 1283–1293  mathscinet  zmath  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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