On the first homology of Peano continua

@article{GregoryR2016,
abstract = {We show that the first homology group of a locally connected compact metric space is either uncountable or finitely generated. This is related to Shelah's well-known result (1988) which shows that the fundamental group of such a space satisfies a similar condition. We give an example of such a space whose fundamental group is uncountable but whose first homology is trivial, showing that our result does not follow from Shelah's. We clarify a claim made by Pawlikowski (1998) and offer a proof of the clarification.},
author = {Gregory R. Conner, Samuel M. Corson},
journal = {Fundamenta Mathematicae},
keywords = {fundamental group; homology group; Polish space; analytic relation},
language = {eng},
number = {1},
pages = {41-48},
title = {On the first homology of Peano continua},
url = {http://eudml.org/doc/283390},
volume = {232},
year = {2016},
}

TY - JOUR
AU - Gregory R. Conner
AU - Samuel M. Corson
TI - On the first homology of Peano continua
JO - Fundamenta Mathematicae
PY - 2016
VL - 232
IS - 1
SP - 41
EP - 48
AB - We show that the first homology group of a locally connected compact metric space is either uncountable or finitely generated. This is related to Shelah's well-known result (1988) which shows that the fundamental group of such a space satisfies a similar condition. We give an example of such a space whose fundamental group is uncountable but whose first homology is trivial, showing that our result does not follow from Shelah's. We clarify a claim made by Pawlikowski (1998) and offer a proof of the clarification.
LA - eng
KW - fundamental group; homology group; Polish space; analytic relation
UR - http://eudml.org/doc/283390
ER -