Strongly quasipositive knots are concordant to infinitely many strongly quasipositive knots

Contact: Aru Ray (aruray @ mpim-bonn.mpg.de)

We show that every non-trivial strongly quasipositive knot is smoothly concordant to infinitely many pairwise non-isotopic strongly quasipositive knots. In contrast to our result, Baader, Dehornoy and Liechti showed that every (topologically locally-flat) concordance class contains at most finitely many positive knots. Moreover, it was conjectured by Baker that smoothly concordant strongly quasipositive fibered knots are isotopic. Our construction uses a satellite operation with companion a slice knot with maximal Thurston-Bennequin number -1. If time permits, we will say a few words about how the construction extends to links.