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.

No abstract

We construct a hyperbolic fibered slice knot with right-veering monodromy, which disproves a conjecture posed in [HKK + 21].

In this paper, we observe that the hat version of the Heegaard Floer invariant of Legendrian knots in contact three-manifolds defined by Lisca-Ozsváth-Stipsicz-Szabó can be combinatorially computed. We rely on Plamenevskaya’s combinatorial description of the Heegaard Floer contact invariant.

Ozsváth, Stipsicz and Szabó define a one-parameter family {Υ K (t)} t∈[0,2] of Heegaard Floer knot invariants for knots K ⊂ S 3 . We generalize Υ K (t) to knots in any rational homology sphere. We study the Υ−invariant of a fibered knot. We prove that the Υ−invariant can never reach its minimum slope if the monodromy of the fibration is not right-veering.