On small homotopies of loops
Geometric Topology
2008-04-27 v1 Algebraic Topology
Group Theory
Abstract
Two natural questions are answered in the negative: (1) If a space has the property that small nulhomotopic loops bound small nulhomotopies, then are loops which are limits of nulhomotopic loops themselves nulhomotopic? (2) Can adding arcs to a space cause an essential curve to become nulhomotopic? The answer to the first question clarifies the relationship between the notions of a space being homotopically Hausdorff and -shape injective.
Keywords
Cite
@article{arxiv.0712.1722,
title = {On small homotopies of loops},
author = {G. Conner and M. Meilstrup and D. Repovš and A. Zastrow and M. Željko},
journal= {arXiv preprint arXiv:0712.1722},
year = {2008}
}
Comments
12 pages, 5 figures