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Polyhedra with virtually polycyclic fundamental groups have finite depth

Danuta Kołodziejczyk (2007)

Fundamenta Mathematicae

The notions of capacity and depth of compacta were introduced by K. Borsuk in the seventies together with some open questions. In a previous paper, in connection with one of them, we proved that there exist polyhedra with polycyclic fundamental groups and infinite capacity, i.e. dominating infinitely many different homotopy types (or equivalently, shapes). In this paper we show that every polyhedron with virtually polycyclic fundamental group has finite depth, i.e., there is a bound on the lengths...

Power-cancellation of CW-complexes with few cells.

Irene Llerena (1992)

Publicacions Matemàtiques

In this paper we use the fact that the rings of integer matrices have the power-substitution property in order to obtain a power-cancellation property for homotopy types of CW-complexes with one cell in dimensions 0 and 4n and a finite number of cells in dimension 2n.

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