Topologically slice knots that are not smoothly slice in any definite 4-manifold

Abstract

We prove that there exist infinitely many topologically slice knots which cannot bound a smooth null-homologous disk in any definite 4-manifold. Furthermore, we show that we can take such knots so that they are linearly independent in the the knot concordance group.

9 pages, 4 figures

References in corpus (4)

• Floer homology and knot complements
• A concordance invariant from the Floer homology of +/- 1 surgeries
• A note on cobordisms of algebraic knots
• A cabling formula for ${\nu }^{+}$ invariant

Cited by in corpus (4)

• A full-twist inequality for the ${\nu }^{+}$-invariant
• An adjunction inequality for the Bauer-Furuta type invariants, with applications to sliceness and 4-manifold topology
• Instantons, special cycles, and knot concordance
• On the slice genus of quasipositive knots in indefinite 4-manifolds