Displaying similar documents to “Shape evaluation groups”

Polyhedra with virtually polycyclic fundamental groups have finite depth

Danuta Kołodziejczyk (2007)

Fundamenta Mathematicae

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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...