Concordance invariants and the Turaev genus
| Autor: | Seungwon Kim, Hongtaek Jung, Sungkyung Kang |
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| Rok vydání: | 2020 |
| Předmět: |
Class (set theory)
010308 nuclear & particles physics General Mathematics Concordance 010102 general mathematics Geometric Topology (math.GT) 01 natural sciences Mathematics::Geometric Topology Combinatorics Mathematics - Geometric Topology Integer Genus (mathematics) Additive function 0103 physical sciences FOS: Mathematics 0101 mathematics 57K10 (Primary) 57K18 (Secondary) Mathematics |
| DOI: | 10.48550/arxiv.2010.00031 |
| Popis: | 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. Comment: 6 pages, 3 figures. Some references are added or corrected. More descriptions on oriented band surgeries and slice-torus invariants are added |
| Databáze: | OpenAIRE |
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