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Mathematics of the USSR-Sbornik, 1981, Volume 38, Issue 2, Pages 255–270
DOI: https://doi.org/10.1070/SM1981v038n02ABEH001327
(Mi sm2450)
 

This article is cited in 2 scientific papers (total in 2 papers)

The fundamental groups of manifolds and Poincaré complexes

V. G. Turaev
References:
Abstract: In this article the fundamental groups of $n$-dimensional manifolds and $n$-dimensional Poincaré; complexes with $[n/2]$-connected universal coverings are studied. Special attention is given to the case $n=3$: it is established that the fundamental groups of closed three-dimensional manifolds possess dual presentations in a certain sense, and purely algebraic conditions are found that are necessary and sufficient for a given group to be isomorphic to the fundamental group of some Poincaré; complex of formal dimension three. With the help of these conditions the symmetry of the Alexander invariants of finite Poincaré; complexes of formal dimension three is established. In the case $n\ne3$ analogous results are proved (the presentations of a group by generators and relations are replaced by segments of resolutions of the fundamental ideal of a group ring, and the Alexander invariants are replaced by their generalizations).
Figures: 1.
Bibliography: 18 titles.
Received: 06.07.1978
Bibliographic databases:
UDC: 513.86
MSC: Primary 57M05; Secondary 57P10
Language: English
Original paper language: Russian
Citation: V. G. Turaev, “The fundamental groups of manifolds and Poincaré complexes”, Math. USSR-Sb., 38:2 (1981), 255–270
Citation in format AMSBIB
\Bibitem{Tur79}
\by V.~G.~Turaev
\paper The fundamental groups of manifolds and Poincar\'e complexes
\jour Math. USSR-Sb.
\yr 1981
\vol 38
\issue 2
\pages 255--270
\mathnet{http://mi.mathnet.ru//eng/sm2450}
\crossref{https://doi.org/10.1070/SM1981v038n02ABEH001327}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=552116}
\zmath{https://zbmath.org/?q=an:0449.57001|0414.57001}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1981LG68600007}
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  • https://doi.org/10.1070/SM1981v038n02ABEH001327
  • https://www.mathnet.ru/eng/sm/v152/i2/p278
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics
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    Abstract page:302
    Russian version PDF:180
    English version PDF:11
    References:46
     
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