Year: 2025
Type: article
Abstract: A Levine (Forum Math. Sigma 4 (2016) art. id. e34) proved the surprising result that there exist knots in homology spheres which are not smoothly concordant to any knot in S 3 , where one allows for concordances in homology cobordisms.Since then subsequent works due to Hom, Levine and Lidman (Duke Math. J. 171 (2022) 3089-3131) and Zhou (J. Topol. 14 (2021) 1369-1395) have strengthened this result showing that there are many knots in homology spheres which are not smoothly concordant to knots in S 3 .In this paper we present evidence that the opposite is true topologically.We study the Whitney tower filtration of concordance (Ann. of Math. 157 (2003) 433-519) and prove that modulo any term in this filtration every knot (or link) in a homology sphere is equivalent to a knot (or link) in S 3 .As an application we recover a result of the author (J. Topol. 13 (2020) 343-355), namely that the solvable filtration similarly fails to distinguish links in homology spheres from links in S 3 .
Source: Algebraic & Geometric Topology
Author: Christopher W Davis
Institution: University of Wisconsin–Eau Claire
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4414971510