Displaying similar documents to “Low dimensional homotopy groups of suspensions of the Hawaiian earring”

A note on generalized equivariant homotopy groups

Marek Golasiński, Daciberg L. Gonçalves, Peter N. Wong (2009)

Banach Center Publications

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In this paper, we generalize the equivariant homotopy groups or equivalently the Rhodes groups. We establish a short exact sequence relating the generalized Rhodes groups and the generalized Fox homotopy groups and we introduce Γ-Rhodes groups, where Γ admits a certain co-grouplike structure. Evaluation subgroups of Γ-Rhodes groups are discussed.

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...