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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 $H_{n - 4} (M, ℋ^{3})$ , where $ℋ^{3}$ 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 $M$ .

Cubical approximation and computation of homology

William Kalies, Konstantin Mischaikow, Greg Watson (1999)

Banach Center Publications

The purpose of this article is to introduce a method for computing the homology groups of cellular complexes composed of cubes. We will pay attention to issues of storage and efficiency in performing computations on large complexes which will be required in applications to the computation of the Conley index. The algorithm used in the homology computations is based on a local reduction procedure, and we give a subquadratic estimate of its computational complexity. This estimate is rigorous in two...

Cubulations, immersions, mappability and a problem of Habegger

Louis Funar (1999)

Annales scientifiques de l'École Normale Supérieure

Cyclic Crystallizations of Spheres.

Javier Bracho (1986)

Manuscripta mathematica

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