We aim at constructing a PL-manifold which is cellularly equivalent to a given homology manifold . The main theorem says that there is a unique obstruction element in , where 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 is compact, we obtain a PL-manifold which is simple homotopy equivalent to .
Nous visons à construire une variété semi-linéaire qui est cellulairement équivalente à une variété homologique donnée. Le théorème dit qu’il y a un élément d’obstruction unique dans , où est un groupe de sphères homologiques qui sont des variétés semi-linéaires. Les éléments triviaux de sont ceux qui sont un bord d’une variété semi-linéaire acyclique. Si l’obstruction est zéro et compacte, nous obtenons une variété semi-linéaire qui est simplement homotopiquement équivalente à .
@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}, pages = {271--286}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {22}, number = {1}, year = {1972}, doi = {10.5802/aif.406}, mrnumber = {49 #1522}, zbl = {0219.57009}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.406/} }
TY - JOUR AU - Sato, Hajime TI - Constructing manifolds by homotopy equivalences I. An obstruction to constructing PL-manifolds from homology manifolds JO - Annales de l'Institut Fourier PY - 1972 SP - 271 EP - 286 VL - 22 IS - 1 PB - Institut Fourier PP - Grenoble UR - http://www.numdam.org/articles/10.5802/aif.406/ DO - 10.5802/aif.406 LA - en ID - AIF_1972__22_1_271_0 ER -
%0 Journal Article %A Sato, Hajime %T Constructing manifolds by homotopy equivalences I. An obstruction to constructing PL-manifolds from homology manifolds %J Annales de l'Institut Fourier %D 1972 %P 271-286 %V 22 %N 1 %I Institut Fourier %C Grenoble %U http://www.numdam.org/articles/10.5802/aif.406/ %R 10.5802/aif.406 %G en %F 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/articles/10.5802/aif.406/
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