On the Upsilon invariant of fibered knots and right-veering open books

Abstract

We give a sufficient condition using the Ozsv\'ath-Stipsicz-Szab\'o concordance invariant Upsilon for the monodromy of the open book decomposition of a fibered knot to be right-veering. As an application, we generalize a result of Baker on ribbon concordances between fibered knots. Following Baker, we conclude that either fibered knots $K$ in $S^{3}$ satisfying that $\Upsilon'(t) = -g(K)$ for some $t \in [0,1)$ are unique in their smooth concordance classes or there exists a counterexample to the Slice-Ribbon Conjecture.