Abstract
We construct an infinite family of topologically slice knots that are not smoothly concordant to their reverses. More precisely, if \(\mathcal {T}\) denotes the concordance group of topologically slice knots and \(\rho \) is the involution of \(\mathcal {T}\) induced by string reversal, then \(\mathcal {T}/ \text {Fix}(\rho )\) contains an infinitely generated free subgroup. The result remains true modulo the subgroup of \(\mathcal {T}\) generated by knots with trivial Alexander polynomial.
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