Homotopy type of planar continua
Algebraic Topology
2017-09-28 v1
Abstract
We prove that the homotopy type of a map from a Peano continuum into a planar or one-dimensional space is determined by the induced homomorphism of fundamental groups. This provides a new proof that planar sets are aspherical and is used to prove that two planar or one-dimensional Peano continua are homotopy equivalent if and only if they have isomorphic fundamental groups.
Cite
@article{arxiv.1709.09211,
title = {Homotopy type of planar continua},
author = {Curtis Kent},
journal= {arXiv preprint arXiv:1709.09211},
year = {2017}
}
Comments
18 pages. Comments welcome