Geodesic
Smooth structures on Poincaré complexes
Izvestiya. Mathematics, Tome 7 (1973) no. 4, pp. 919-932 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{IM2_1973_7_4_a7,
     author = {S. B. Shlosman},
     title = {Smooth structures on {Poincar\'e} complexes},
     journal = {Izvestiya. Mathematics},
     pages = {919--932},
     year = {1973},
     volume = {7},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1973_7_4_a7/}
}
TY  - JOUR
AU  - S. B. Shlosman
TI  - Smooth structures on Poincaré complexes
JO  - Izvestiya. Mathematics
PY  - 1973
SP  - 919
EP  - 932
VL  - 7
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/IM2_1973_7_4_a7/
LA  - en
ID  - IM2_1973_7_4_a7
ER  - 
%0 Journal Article
%A S. B. Shlosman
%T Smooth structures on Poincaré complexes
%J Izvestiya. Mathematics
%D 1973
%P 919-932
%V 7
%N 4
%U http://geodesic.mathdoc.fr/item/IM2_1973_7_4_a7/
%G en
%F IM2_1973_7_4_a7
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/

[1] Mischenko A. S., “Gomotopicheskaya invariantnost vysshikh signatur”, Izv. AN SSSR. Ser. matem., 35 (1971), 1316–1355 | Zbl

[2] Mischenko A. S., “Perestroiki kompleksov Puankare”, Matem. sb., 85:3 (1971), 367–372

[3] Spivak M., “Spaces, satisfying Poincare duality”, Topology, 6 (1967), 77–102 | DOI | MR

[4] Wall C. T. C., Surgery of compact manifolds, Preprint, Liverpool Univ., 1969

[5] Wall C. T. C., “Poincare complexes, I”, Ann. Math., 86:2 (1967), 213–245 | DOI | MR | Zbl

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