Rasmussen and Ozsváth–Szabó invariants of a family of general pretzel knots

Abstract

We compute integer valued knot concordance invariants of a family of general pretzel knots if the invariants are equal to the negative values of signatures for alternating knots. Examples of such invariants are Rasmussen s-invariants and twice Ozsváth–Szabó knot Floer homology τ-invariants. We use the crossing change inequalities of Livingston and the fact that pretzel knots are almost alternating. As a consequence, for the family of pretzel knots given in this paper, s-invariants are twice τ-invariants.