Linear independence of rationally slice knots

Abstract

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.

arXiv comment21 pages, 4 figures, final version, to appear in Geometry & Topology

References in corpus (21)

• Floer homology and knot complements
• Knot Floer homology and the four-ball genus
• Bordered Heegaard Floer homology: Invariance and pairing
• Concordance homomorphisms from knot Floer homology
• The knot Floer complex and the smooth concordance group
• Cables of thin knots and bordered Heegaard Floer homology
• Involutive Heegaard Floer homology
• Gauge theory and Rasmussen's invariant
• The structure of the rational concordance group of knots
• Link cobordisms and functoriality in link Floer homology
• A slice genus lower bound from sl(n) Khovanov-Rozansky homology
• A note on Gornik's perturbation of Khovanov-Rozansky homology
• Connected sums and involutive knot Floer homology
• More concordance homomorphisms from knot Floer homology
• Cabling in terms of immersed curves
• Applications of involutive Heegaard Floer homology
• Knot Floer homology and the unknotting number
• Upsilon-like concordance invariants from sl(n) knot cohomology
• An infinite-rank summand of the homology cobordism group
• On rational sliceness of Miyazaki's fibered, $-$amphicheiral knots
• A mnemonic for the Lipshitz-Ozsváth-Thurston correspondence