Work

Topologically and rationally slice knots

Year: 2025

Type: article

Abstract: A knot in $$S^3$$ S 3 is topologically slice if it bounds a locally flat disk in $$B^4$$ B 4 . A knot in $$S^3$$ S 3 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 $$\mathbb {Z}^\infty $$ 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.

Source: Selecta Mathematica

DOI: 10.1007/s00029-025-01020-1

Authors: Jennifer Hom, Sungkyung Kang, JungHwan Park

Institutions: Georgia Institute of Technology, University of Oxford, Institute for Basic Science, Korea Advanced Institute of Science and Technology

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

OpenAlex ID: W4408058101

FWCI:

Cites: 27

Cited by: 1

Related to: 10