Concordance Invariants and the Turaev Genus

Abstract

We show that the differences between various concordance invariants of knots, including Rasmussen's s-invariant and its generalizations s(n)-invariants, give lower bounds to the Turaev genus of knots. Using the fact that our bounds are nontrivial for some quasi-alternating knots, we show the additivity of Turaev genus for a certain class of knots. This leads us to the 1st example of an infinite family of quasi-alternating knots with Turaev genus exactly g for any fixed positive integer g, solving a question of Champanerkar-Kofman.