Geodesic
On an invariant of open manifolds
Izvestiya. Mathematics , Tome 1 (1967) no. 5, pp. 1041-1054.

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The combinatorial invariance of the obstruction $\Delta$ is proved and a Poincaré duality relation is derived for $\Delta$. It is shown that the invariant $\Delta$ is a meaningful concept, i.e., that there exist open manifolds for which $\Delta\ne0$. The results that are obtained are used for the construction of a boundary for an open manifold and for the fibering of a closed smooth manifold over a circle. 
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V. L. Golo. On an invariant of open manifolds. Izvestiya. Mathematics , Tome 1 (1967) no. 5, pp. 1041-1054. http://geodesic.mathdoc.fr/item/IM2_1967_1_5_a6/

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