The homotopy dimension of codiscrete subsets of the 2-sphere

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We characterize those planar Peano continua that are homotopy equivalent to 1-dimensional sets. While many planar Peano continua are not homotopically 1-dimensional, we prove that each has fundamental group that embeds in the fundamental group of a 1-dimensional planar Peano continuum. We leave open the following question: Is a planar Peano continuum homotopically 1- dimensional if its fundamental group is isomorphic with the fundamental group of a 1-dimensional planar Peano continuum?
18 pages, 2 figures

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Geometric Topology, Algebraic Topology, 54F50;55M10

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http://salesiana.dossiersoluciones.com/handle/123456789/110043

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0603069
 http://arxiv.org/abs/math/0603069

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arXiv