Whitney tower concordance and knots in homology spheres

Christopher William Davis

doi:10.2140/agt.2025.25.3503

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arXiv · 2303.14509

Whitney tower concordance and knots in homology spheres

Christopher William Davis

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Abstract

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 $S^3$, 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 $S^3$. 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 $S^3$. 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 $S^3$.

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BibTeX RIS

Christopher William Davis. 2023-03-25. Whitney tower concordance and knots in homology spheres. https://doi.org/10.2140/agt.2025.25.3503

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