Concordance, Crossing Changes, and Knots in Homology Spheres
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Publication:5148073
DOI10.4153/S0008439519000791zbMATH Open1462.57002arXiv1903.09225MaRDI QIDQ5148073
Author name not available (Why is that?)
Publication date: 29 January 2021
Published in: (Search for Journal in Brave)
Abstract: Any knot in may be reduced to a slice knot by crossing changes. Indeed, this slice knot can be taken to be the unknot. In this paper we study the question of when the same holds for knots in homology spheres. We show that a knot in a homology sphere is nullhomotopic in a smooth homology ball if and only if that knot is smoothly concordant to a knot which is homotopic to a smoothly slice knot. As a consequence, we prove that the equivalence relation on knots in homology spheres given by cobounding immersed annuli in a homology cobordism is generated by concordance in homology cobordisms together with homotopy in a homology sphere.
Full work available at URL: https://arxiv.org/abs/1903.09225
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