This article is cited in 2 scientific papers (total in 2 papers)
The fundamental groups of manifolds and Poincaré complexes
V. G. Turaev
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).
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Mathematics of the USSR-Sbornik, 1981, 38:2, 255–270
MSC: Primary 57M05; Secondary 57P10
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
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\paper The fundamental groups of manifolds and Poincar\'e complexes
\jour Mat. Sb. (N.S.)
\jour Math. USSR-Sb.
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This publication is cited in the following articles:
Turaev V., “3-Dimensional Poincaré Complexes - Classification and Splitting”, 257, no. 3, 1981, 551–552
V. G. Turaev, “Three-dimensional Poincaré complexes: homotopy classification and splitting”, Math. USSR-Sb., 67:1 (1990), 261–282
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