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On the planarity of infinite 2-complexes

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Abstract

This paper is devoted to the problem of characterizing infinite planar polyhedra. We give two topological characterizations of planarity, and two others of proper planarity (embeddings with no accumulation points). We also give a combinatorial characterization of planarity, and proper planarity. In the case of compact polyhedra both results provide a weaker condition than that given by Gross and Rosen in [6].

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Authors and Affiliations

  1. Dept. Matemática Aplicada I, Facultad de In-formática, Universidad de Sevilla, Avda. Reina Mercedes s/n, 41012-Sevilla, Spain

    A. M’arquez

  2. Dept. Geometría y Topología, Facultad de Matemáticas, Universidad de Sevilla, Apdo. 1160, 41080-Sevilla, Spain

    R. Ayala & A. Quintero

Authors
  1. A. M’arquez
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  2. R. Ayala
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  3. A. Quintero
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Correspondence to A. M’arquez or R. Ayala.

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M’arquez, A., Ayala, R. & Quintero, A. On the planarity of infinite 2-complexes. Abh.Math.Semin.Univ.Hambg. 67, 137–148 (1997). https://doi.org/10.1007/BF02940824

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