Ends of non-metrizable manifolds: a generalized bagpipe theorem
General Topology
2022-01-27 v5 Geometric Topology
Logic
Abstract
We initiate the study of ends of non-metrizable manifolds and introduce the notion of short and long ends. Using the theory developed, we provide a characterization of (non-metrizable) surfaces that can be written as the topological sum of a metrizable manifold plus a countable number of "long pipes" in terms of their spaces of ends; this is a direct generalization of Nyikos's bagpipe theorem.
Cite
@article{arxiv.2004.10913,
title = {Ends of non-metrizable manifolds: a generalized bagpipe theorem},
author = {David Fernández-Bretón and Nicholas G. Vlamis and Mathieu Baillif},
journal= {arXiv preprint arXiv:2004.10913},
year = {2022}
}
Comments
39 pages, 4 figures. Main paper written by the first two authors, Appendix B written by all three