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Izv. Akad. Nauk SSSR Ser. Mat., 1982, Volume 46, Issue 1, Pages 36–55 (Mi izv1604)  

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

Mappings of free $\mathbf Z_p$-spaces into manifolds

A. Yu. Volovikov


Abstract: This paper considers generalizations of the Bourgin–Yang theorem. It is shown that if $f\colon X\to M$ is a continuous mapping of a paracompact free $\mathbf Z_p$-space $X$ into an $m$-dimensional manifold $M$, then, under the condition that $\operatorname{in}X\geqslant n>m(p-1)$ (where $\operatorname{in}X$ is the index in the sense of Yang) and $f^*V_i=0$ for $i\geqslant1$, where the $V_i$ are the Wu classes of $M$, the following inequality holds:
$$ \operatorname{in}\{x\in X\mid f(x)=f(gx) \forall g\in\mathbf Z_p\}\geqslant n-m(p-1). $$

Besides this result, certain “nonsymmetric” versions of the Borsuk–Ulam theorem are proved.
Bibliography: 16 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1983, 20:1, 35–53

Bibliographic databases:

UDC: 513.83
MSC: Primary 55M20; Secondary 55N25, 57S17
Received: 09.12.1980

Citation: A. Yu. Volovikov, “Mappings of free $\mathbf Z_p$-spaces into manifolds”, Izv. Akad. Nauk SSSR Ser. Mat., 46:1 (1982), 36–55; Math. USSR-Izv., 20:1 (1983), 35–53

Citation in format AMSBIB
\Bibitem{Vol82}
\by A.~Yu.~Volovikov
\paper Mappings of free $\mathbf Z_p$-spaces into manifolds
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1982
\vol 46
\issue 1
\pages 36--55
\mathnet{http://mi.mathnet.ru/izv1604}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=643892}
\zmath{https://zbmath.org/?q=an:0503.55001}
\transl
\jour Math. USSR-Izv.
\yr 1983
\vol 20
\issue 1
\pages 35--53
\crossref{https://doi.org/10.1070/IM1983v020n01ABEH001338}


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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. Yu. Volovikov, “A theorem of Bourgin–Yang type for $\mathbb{Z}_p^n$-action”, Russian Acad. Sci. Sb. Math., 76:2 (1993), 361–387  mathnet  crossref  mathscinet  zmath  isi
    2. D. V. Bolotov, “The Cohen–Lusk Conjecture”, Math. Notes, 70:1 (2001), 20–24  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. A. Yu. Volovikov, “Coincidence points of maps of $\mathbb Z_p^n$-spaces”, Izv. Math., 69:5 (2005), 913–962  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. A. Yu. Volovikov, E. V. Shchepin, “Antipodes and embeddings”, Sb. Math., 196:1 (2005), 1–28  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    5. M. C. Crabb, J. Jaworowski, “Aspects of the Borsuk–Ulam theorem”, J. Fixed Point Theory Appl, 2013  crossref
    6. Benjamin Matschke, “A parametrized version of the Borsuk–Ulam–Bourgin–Yang–Volovikov theorem”, J. Topol. Anal, 2014, 1  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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