Geodesic
Smooth structures on Poincar\'e complexes
Izvestiya. Mathematics , Tome 7 (1973) no. 4, pp. 919-932

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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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     author = {S. B. Shlosman},
     title = {Smooth structures on {Poincar\'e} complexes},
     journal = {Izvestiya. Mathematics },
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     number = {4},
     year = {1973},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1973_7_4_a7/}
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S. B. Shlosman. Smooth structures on Poincar\'e complexes. Izvestiya. Mathematics , Tome 7 (1973) no. 4, pp. 919-932. http://geodesic.mathdoc.fr/item/IM2_1973_7_4_a7/