Weakly Chained Spaces
Algebraic Topology
2021-03-16 v7 Group Theory
Abstract
We introduce "weakly chained spaces", which need not be locally connected or path connected, but for which one has a reasonable notion of generalized fundamental group and associated generalized universal cover. We show that in the compact metric case, weakly chained is equivalent to the concept of "pointed 1-movable" from classical shape theory. We use this fact and a theorem of Geoghegan-Swenson to give criteria on the metric spheres in a CAT(0) space that imply that the boundary is has semistable fundamental group at infinity.
Cite
@article{arxiv.2001.03112,
title = {Weakly Chained Spaces},
author = {Conrad Plaut},
journal= {arXiv preprint arXiv:2001.03112},
year = {2021}
}
Comments
This version corrects some minor errors