Concordance invariants and the Turaev genus

Hongtaek Jung; Sungkyung Kang; Seungwon Kim

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arXiv · 2010.00031

Concordance invariants and the Turaev genus

Hongtaek Jung·Sungkyung Kang·Seungwon Kim

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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 first 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.

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Hongtaek Jung, Sungkyung Kang, Seungwon Kim. 2020-09-30. Concordance invariants and the Turaev genus. https://arxiv.org/abs/2010.00031

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