Constructing manifolds by homotopy equivalences I. An obstruction to constructing PL-manifolds from homology manifolds
Annales de l'Institut Fourier, Volume 22 (1972) no. 1, p. 271-286

We aim at constructing a PL-manifold which is cellularly equivalent to a given homology manifold M n . The main theorem says that there is a unique obstruction element in H n-4 (M, 3 ), where 3 is the group of 3-dimensional PL-homology spheres modulo those which are the boundary of an acyclic PL-manifold. If the obstruction is zero and M is compact, we obtain a PL-manifold which is simple homotopy equivalent to M.

Nous visons à construire une variété semi-linéaire qui est cellulairement équivalente à une variété homologique M n donnée. Le théorème dit qu’il y a un élément d’obstruction unique dans H n-4 (M; 3 ), où 3 est un groupe de sphères homologiques qui sont des variétés semi-linéaires. Les éléments triviaux de 3 sont ceux qui sont un bord d’une variété semi-linéaire acyclique. Si l’obstruction est zéro et M compacte, nous obtenons une variété semi-linéaire qui est simplement homotopiquement équivalente à M.

@article{AIF_1972__22_1_271_0,
     author = {Sato, Hajime},
     title = {Constructing manifolds by homotopy equivalences I. An obstruction to constructing PL-manifolds from homology manifolds},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Louis-Jean},
     address = {Gap},
     volume = {22},
     number = {1},
     year = {1972},
     pages = {271-286},
     doi = {10.5802/aif.406},
     zbl = {0219.57009},
     mrnumber = {49 \#1522},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1972__22_1_271_0}
}
Sato, Hajime. Constructing manifolds by homotopy equivalences I. An obstruction to constructing PL-manifolds from homology manifolds. Annales de l'Institut Fourier, Volume 22 (1972) no. 1, pp. 271-286. doi : 10.5802/aif.406. http://www.numdam.org/item/AIF_1972__22_1_271_0/

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