A diagrammatic approach to the Rasmussen invariant via tangles and cobordisms

Abstract

We introduce a diagrammatic approach to Rasmussen's $s$-invariant, based on Bar-Natan's reformulation of Khovanov homology for tangles and cobordisms. This method enables a local computation of $s$ from a tangle decomposition of a knot diagram. As an application, we compute the $s$-invariants of all 3-strand pretzel knots.

66 pages. v3: KK added as a coauthor; Section 5 added to describe the computation of 3-strand pretzel knots