Displaying similar documents to “Fundamental groups of one-dimensional spaces”

Homotopy types of one-dimensional Peano continua

Katsuya Eda (2010)

Fundamenta Mathematicae

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Let X and Y be one-dimensional Peano continua. If the fundamental groups of X and Y are isomorphic, then X and Y are homotopy equivalent. Every homomorphism from the fundamental group of X to that of Y is a composition of a homomorphism induced from a continuous map and a base point change isomorphism.

Variations on a theme of homotopy

Timothy Porter (2013)

Annales de la faculté des sciences de Toulouse Mathématiques

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The aim of this article is to bring together various themes from fairly elementary homotopy theory and to examine them, in part, from a historical and philosophical viewpoint.

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...

Homotopy dominations within polyhedra

Danuta Kołodziejczyk (2003)

Fundamenta Mathematicae

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We show the existence of a finite polyhedron P dominating infinitely many different homotopy types of finite polyhedra and such that there is a bound on the lengths of all strictly descending sequences of homotopy types dominated by P. This answers a question of K. Borsuk (1979) dealing with shape-theoretic notions of "capacity" and "depth" of compact metric spaces. Moreover, π₁(P) may be any given non-abelian poly-ℤ-group and dim P may be any given integer n ≥ 3.