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This article is cited in 2 scientific papers (total in 2 papers)
The fundamental groups of manifolds and Poincaré complexes
V. G. Turaev
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
Citation:
V. G. Turaev, “The fundamental groups of manifolds and Poincaré complexes”, Mat. Sb. (N.S.), 110(152):2(10) (1979), 278–296; Math. USSR-Sb., 38:2 (1981), 255–270
Linking options:
https://www.mathnet.ru/eng/sm2450https://doi.org/10.1070/SM1981v038n02ABEH001327 https://www.mathnet.ru/eng/sm/v152/i2/p278
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Abstract page: | 279 | Russian version PDF: | 177 | English version PDF: | 6 | References: | 38 |
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