Explicit formula for the Rasmussen invariant of odd pretzel knots

Abstract

We compute the Rasmussen s-invariant for all odd pretzel knots, giving an explicit closed formula. The formula extends to all slice-torus invariants that are invariant under mutation. In the absence of mutation invariance, we prove the formula under a mild condition on the pretzel parameters, which we conjecture to be unnecessary.

arXiv comment10 pages, 7 figures