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 ${{\rm Y}}^{\prime }(t)=-g(K)$ for some $t\in [0,1)$ are unique in their smooth concordance classes or there exists a counterexample to the Slice-Ribbon Conjecture.

16 pages, 3 figures

References in corpus (1)

• Some remarks on cabling, contact structures, and complex curves