The dealternating number and the alternation number of a closed 3-braid

2008/08/05 by Tetsuya Abe, Kengo Kishimoto, Abe, Tetsuya +1 · 2 citations
Mathematics · #57M25 #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.0808.0573

openalex publication_date 2008/08/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give an upper bound for the dealternating number of a closed 3-braid. As applications, we determine the dealternating numbers, the alternation numbers and the Turaev genera of some closed positive 3-braids. We also show that there exist infinitely many positive knots with any dealternating number (or any alternation number) and any braid index.

Cited by

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

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