Homomorphims from the fundamental group of planar sets
Algebraic Topology
2018-03-28 v2 Geometric Topology
Abstract
We prove that every homomorphism from the fundamental group of a planar Peano continuum to the fundamental group of a planar or one-dimensional Peano continuum is induced by a continuous map up to conjugation. This is then used to provide a family of uncountable many planar Peano continua with pairwise non-isomorphic fundamental groups all of which are not homotopy equivalent to a one-dimensional space.
Keywords
Cite
@article{arxiv.1305.4215,
title = {Homomorphims from the fundamental group of planar sets},
author = {Curt Kent},
journal= {arXiv preprint arXiv:1305.4215},
year = {2018}
}
Comments
This is a short note showing how to extend a previous paper by the author and Greg Conner to the planar setting