The homotopy dimension of codiscrete subsets of the 2-sphere
Geometric Topology
2007-05-23 v1 Algebraic Topology
Abstract
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?
Keywords
Cite
@article{arxiv.math/0603069,
title = {The homotopy dimension of codiscrete subsets of the 2-sphere},
author = {J. W. Cannon and G. R. Conner},
journal= {arXiv preprint arXiv:math/0603069},
year = {2007}
}
Comments
18 pages, 2 figures