On the virtual Rasmussen invariant

Abstract

We produce chain-level generators of the virtual Lee complex $ Kh ' (V ) $ and use them to convert the computable bounds on the Rasmussen invariant of classical knots due to Kawamura and Lobb into bounds on the virtual Rasmussen invariant as defined by Dye, Kaestner, and Kauffman. We also exhibit a class of diagrams for which the bounds are tight. In addition, we use the chain-level generators to show that the virtual Rasmussen invariant is additive with respect to connect sum.