We show that the Bruschlinsky group with the winding order is a homomorphism invariant for a class of one-dimensional inverse limit spaces. In particular we show that if a presentation of an inverse limit space satisfies the Simplicity Condition, then the Bruschlinsky group with the winding order of the inverse limit space is a dimension group and is a quotient of the dimension group with the standard order of the adjacency matrices associated with the presentation.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm170-3-5,
author = {Inhyeop Yi},
title = {Ordered group invariants for one-dimensional spaces},
journal = {Fundamenta Mathematicae},
volume = {167},
year = {2001},
pages = {267-286},
zbl = {0983.37012},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm170-3-5}
}
Inhyeop Yi. Ordered group invariants for one-dimensional spaces. Fundamenta Mathematicae, Tome 167 (2001) pp. 267-286. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm170-3-5/