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

Abstract

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.