Linear independence of rationally slice knots

Hom, Jennifer¹ ; Kang, Sungkyung² ; Park, JungHwan³ ; Stoffregen, Matthew⁴

¹ School of Mathematics, Georgia Institute of Technology, Atlanta, GA, United States
² Sungkyung Kang, Center For Geometry and Physics, Institute of Basic Science, Pohang, South Korea
³ Department of Mathematical Sciences, KAIST, Daejeon, South Korea
⁴ Department of Mathematics, Michigan State University, East Lansing, MI, United States

Geometry & topology, Tome 26 (2022) no. 7, pp. 3143-3172.

Résumé

A knot in $S^3$ is rationally slice if it bounds a disk in a rational homology ball. We give an infinite family of rationally slice knots that are linearly independent in the knot concordance group. In particular, our examples are all infinite order. All previously known examples of rationally slice knots were order two.

Détail

DOI : 10.2140/gt.2022.26.3143

Keywords: rationally slice knot, linear independence, involutive knot Floer homology

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