We use classical techniques to answer some questions raised by Daniele Celoria about almost-concordance of knots in arbitrary closed –manifolds. We first prove that, given , for any nontrivial element there are infinitely many distinct smooth almost-concordance classes in the free homotopy class of the unknot. In particular we consider these distinct smooth almost-concordance classes on the boundary of a Mazur manifold and we show none of these distinct classes bounds a PL–disk in the Mazur manifold, but all the representatives we construct are topologically slice. We also prove that all knots in the free homotopy class of in are smoothly concordant.
"A note on knot concordance." Algebr. Geom. Topol. 18 (5) 3119 - 3128, 2018. https://doi.org/10.2140/agt.2018.18.3119