arXiv:math/0603069 Abstract

arXiv:math/0603069 [math.GT]Abstract References Reviews Resources

The homotopy dimension of codiscrete subsets of the 2-sphere

Published 2006-03-03Version 1

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?

Comments: 18 pages, 2 figures

Categories: math.GT, math.AT

Subjects: 54F50, 55M10

Keywords: fundamental group, codiscrete subsets, homotopy dimension, homotopy equivalent, leave open

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