Constructing manifolds by homotopy equivalences I. An obstruction to constructing PL-manifolds from homology manifolds

Sato, Hajime. "Constructing manifolds by homotopy equivalences I. An obstruction to constructing PL-manifolds from homology manifolds." Annales de l'institut Fourier 22.1 (1972): 271-286. <http://eudml.org/doc/74068>.

@article{Sato1972,
abstract = {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 $H_\{n-4\}(M,\{\cal H\}^3)$, where $\{\cal H\}^3$ 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 $M$.},
author = {Sato, Hajime},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {1},
pages = {271-286},
publisher = {Association des Annales de l'Institut Fourier},
title = {Constructing manifolds by homotopy equivalences I. An obstruction to constructing PL-manifolds from homology manifolds},
url = {http://eudml.org/doc/74068},
volume = {22},
year = {1972},
}

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
PB - Association des Annales de l'Institut Fourier
VL - 22
IS - 1
SP - 271
EP - 286
AB - 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 $H_{n-4}(M,{\cal H}^3)$, where ${\cal H}^3$ 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 $M$.
LA - eng
UR - http://eudml.org/doc/74068
ER -