| On small homotopies of loops (2007) | |||||||||
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 $\pi_1$-shape injective.. Comment: 12 pages, 5 figures | |||||||||
Details der Publikation | |||||||||
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