2023/03/25 by Christopher William Davis, Davis, Christopher William
Mathematics · Medicine · #57K10 #57N70 #Botulinum Toxin and Related Neurological Disorders #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2303.14509
openalex publication_date 2023/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02
In a groundbreaking work A. Levine proved the surprising result that there exist knots in homology spheres which are not smoothly concordant to any knot in S3, even if one allows for concordances in homology cobordisms. Since then subsequent works due to Hom-Levine-Lidman and Zhou have strengthened this result showing that there are many knots in homology spheres which are not smoothly concordant to knots in S3. In this paper we present evidence that the opposite is true topologically. We study the Whitney tower filtration of concordance due to Cochran-Orr-Teichner 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 S3. As an application we recover the main result of [Davis2019], namely that the solvable filtration similarly fails to distinguish links in homology spheres from links in S3.