Geodesic
Smooth structures on Poincaré complexes
Izvestiya. Mathematics, Tome 7 (1973) no. 4, pp. 919-932 
S. B. Shlosman. Smooth structures on Poincaré complexes. Izvestiya. Mathematics, Tome 7 (1973) no. 4, pp. 919-932. http://geodesic.mathdoc.fr/item/IM2_1973_7_4_a7/
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     author = {S. B. Shlosman},
     title = {Smooth structures on {Poincar\'e} complexes},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The main theorem states that if the Spivak normal fibration associated to a Poincaré complex admits a vector bundle structure, then the Poincaré complex is homotopy equivalent to the union of two smooth manifolds with their boundaries identified via a homotopy equivalence. The theorem is applied to the question of existence of smooth structures on Poincaré complexes.

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[6] Shlosman S. B., “Podmnogoobraziya korazmernosti odin i prostoi gomotopicheskii tip”, Matem. zametki, 12:2 (1972), 167–175 | Zbl