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

Abstract

We give a sufficient condition using the Ozsváth-Stipsicz-Szabó 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 Υ (t) = −g(K) for some t ∈ [0, 1) are unique in their smooth concordance classes or there exists a counterexample to the Slice-Ribbon Conjecture.