Concordance invariants and the Turaev genus

2020/09/30 by Jung, Hongtaek, Kang, Sungkyung, Kim, Seungwon · 2 citations
#57K10 (Primary) 57K18 (Secondary) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2010.00031

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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• On the arc index and Turaev genus of a link
• A characterization of adequate Turaev genus one links

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