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Izv. Akad. Nauk SSSR Ser. Mat., 1979, Volume 43, Issue 5, Pages 1004–1024 (Mi izv1745)  

This article is cited in 3 scientific papers (total in 3 papers)

On real homotopy properties of complete intersections

I. K. Babenko


Abstract: The real homotopy type of complete intersections in $\mathbf CP^N$ is studied. It is proved that these manifolds are intrinsically formal in the sense of Stashev and Gal'perin. The Poincaré series of the loop space on complete intersections is computed, and thus the validity of the Serre conjecture on the rationality for such complexes is established. As a corollary, a formula for the rational homotopy groups of a complete intersection is obtained.
Bibliography: 12 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1980, 15:2, 241–258

Bibliographic databases:

UDC: 513.6
MSC: Primary 55P15, 55P35, 14F25; Secondary 14E30, 13N05, 55T05, 55T10
Received: 03.05.1979

Citation: I. K. Babenko, “On real homotopy properties of complete intersections”, Izv. Akad. Nauk SSSR Ser. Mat., 43:5 (1979), 1004–1024; Math. USSR-Izv., 15:2 (1980), 241–258

Citation in format AMSBIB
\Bibitem{Bab79}
\by I.~K.~Babenko
\paper On real homotopy properties of complete intersections
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1979
\vol 43
\issue 5
\pages 1004--1024
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=552549}
\zmath{https://zbmath.org/?q=an:0443.14012|0423.14011}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1980IzMat..15..241B}
\transl
\jour Math. USSR-Izv.
\yr 1980
\vol 15
\issue 2
\pages 241--258
\crossref{https://doi.org/10.1070/IM1980v015n02ABEH001222}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1980LD11600002}


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  • http://mi.mathnet.ru/eng/izv1745
  • http://mi.mathnet.ru/eng/izv/v43/i5/p1004

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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. I. K. Babenko, “Problems of growth and rationality in algebra and topology”, Russian Math. Surveys, 41:2 (1986), 117–175  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. R. L. Krasauskas, Yu. P. Solov'ev, “Rational Hermitian $K$-theory and dihedral homology”, Math. USSR-Izv., 33:2 (1989), 261–293  mathnet  crossref  mathscinet  zmath
    3. I. K. Babenko, “Topological entropy of geodesic flows on simply connected manifolds, and related topics”, Izv. Math., 61:3 (1997), 517–535  mathnet  crossref  crossref  mathscinet  zmath  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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