Work

Torsion in the knot concordance group and cabling

Year: 2024

Type: article

Abstract: We define a nontrivial modulo 2 valued additive concordance invariant defined on the torsion subgroup of the knot concordance group using involutive knot Floer package. For knots not contained in its kernel, we prove that their iterated (\mathrm{odd},1) -cables have infinite order in the concordance group and, among them, infinitely many are linearly independent. Furthermore, by taking (2,1) -cables of the aforementioned knots, we present an infinite family of knots which are strongly rationally slice but not slice.

Source: Journal of the European Mathematical Society

DOI: 10.4171/jems/1520

Authors: Sungkyung Kang, JungHwan Park

Institutions: 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: diamond

OpenAlex ID: W4401884657

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