An infinite-rank summand of knots with trivial Alexander polynomial (Q668772)

Briefly explaining the Heegaard Floer homology of closed oriented 3-manifolds, the knot Floer homology of knots in \(S^3\), and various resultant smooth knot concordance invariants, this paper proves that there exists an infinite-rank summand in the subgroup of the knot concordance group generated by knots with trivial Alexander polynomial, using the upsilon-invariant introduced by \textit{P. S. Ozsváth}, \textit{A. I. Stipsicz} and \textit{Z. Szabó} [Adv. Math. 315, 366--426 (2017; Zbl 1383.57020)]and giving a sufficient condition for two satellite knots to have identical upsilon-invariant.