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.

中文翻译：

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一致性不变量和 Turaev 属

我们证明了结的各种一致性不变量之间的差异，包括 Rasmussen 的 $s$-invariant 及其推广 $s_n$-invariants，为 Turaev 类的结提供了下界。利用我们的界限对于某些准交替结来说是非平凡的这一事实，我们展示了 Turaev 属对某一类结的可加性。这将我们引向了第一个具有 Turaev 属的准交替结的无限族的第一个例子，对于任何固定的正整数 $g$，它解决了 Champanerkar-Kofman 的问题。