2023/04/13 by Jennifer Hom, Hom, Jennifer, Sungkyung Kang +3 · 1 citation
Mathematics · #57K10 #57K18 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2304.06265
openalex publication_date 2023/04/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A knot in S3 is topologically slice if it bounds a locally flat disk in B4. A knot in S3 is rationally slice if it bounds a smooth disk in a rational homology ball. We prove that the smooth concordance group of topologically and rationally slice knots admits a ℤ^∞ subgroup. All previously known examples of knots that are both topologically and rationally slice were of order two. As a direct consequence, it follows that there are infinitely many topologically slice knots that are strongly rationally slice but not slice.